The Third CS Corps was also known as Hill’s Corps. The unit was commanded by General James Longstreet (November 9, 1825 – April 2, 1865). Longstreet was a career U.S. Army officer in the Mexican–American War and Seminole Wars and a Confederate general in the American Civil War. He gained early fame as the commander of the "Light Division" in the Seven Days Battles and became one of Stonewall Jackson's ablest subordinates, distinguishing himself in the 1862 battles of Cedar Mountain, Second Bull Run, Antietam, and Fredericksburg.
Following Jackson's death in May 1863 at the Battle of Chancellorsville, Hill was promoted to lieutenant general and commanded the Third Corps of Robert E. Lee's Army of Northern Virginia, which he led in the Gettysburg Campaign and the fall campaigns of 1863. His command of the corps in 1864–65 was interrupted on multiple occasions by illness, from which he did not return until just before the end of the war, when he was killed during the Union Army offensive at the Third Battle of Petersburg.
The Hill's C.S. Marker - Headquarters Marker is located on the right or west side of West Confederate Avenue at McMillian Woods, along Seminary Ridge. The monument is near the North Carolina and Tennessee State Memorials, faces the east and is a few feet from the edge of the road. 
Parking is available at the side of the road at small, intermittently placed cutouts. Please do not park on the grass, park on the side of the road. You will be ticketed. I visited this monument on Saturday, March 10, 2012 at 1:16 PM, just before the clocks were set ahead for the Spring.
The monument was erected in 1907, according to the NPS/NRHP narrative. Another source has it at 1920. It is simply amazing with all the work put into these monuments, not one person had the wherewithal or simple presence of mind to write down the dedication dates or manufacturing dates. I know for sure the work was done under the direction of the Gettysburg National Park Commission (established by the United States Department of War), after they took over the administration of the park from the Gettysburg Battlefield Memorial Association (whose funds had expired) on March 3, 1893, and whose stewardship was then transferred to the National Park Service in 1933, which entity still operates the park today). SOURCE
Description
Draw the Sword, with descriptive help from the NPS site (and me), offers the following description: Erected by the Gettysburg National Parks Commission and completed in 1920-1921; consists of bronze cannon mounted on a granite base. Denotes the approximate location of A.P. Hill’s headquarters, which were actually located behind Seminary Ridge. 12-pounder bronze Confederate cannon cemented into hexagonal granite base w/ muzzle up. Overall height, 10’6?. 2 bronze inscription tablets on E face. Bronze plate w/ “C.S.A.” inscribed, fastened across gun at trunnion.
My SOURCE for all things weapons at Gettysburg provided me additional information about this weapon which I was unable to make out due to the muzzle stamp being so high up in the air. I learned about the registry number from the Historical Marker Database (citation below). The registry number allowed me to learn about the rest of the manufacturing information. The line of information below appears in order exactly as it appears on the muzzle, starting at the top and moving clockwise.
No 98AF - 1864 - 1248 - GWR
No 98AF Refers to the Army registration number, a way for the military to keep track of the guns when they take receipt of them from the various Confederate foundries. The AF refers refers to the Augusta Foundry (Govt Foundry & Machine Works) in Augusta GA and the place where this gun was manufactured. (More on that below) 1864 refers to the production date. 1248 refers to the weight of the firing tube. This number is on the bottom of the muzzle. Each gun is usually very unique and has its own weight which distinguishes it from every other gun, like a fingerprint. INSP GWR refers to the military officer responsible for inspecting the final product to make sure it meets all standards. After a heck of a lot of searching about these initials I discovered the following passage: George Washington Rains: Colonel commanding Augusta Arsenal, Augusta Powder Mills, and Augusta Foundry and Machine Works (q.v.). Initials "G.W.R." are generally coupled with "A.F." (Augusta Foundry). I would surmise then George Washington Rains surveyed all the weapons produced from the foundry and was in charge of quality control. SOURCE. The carriages were approximately 900 pounds which makes this entire weapon 2,100 pounds.
About the Foundry
The Augusta Foundry was one of several “government” foundries established during the war to furnish ordnance to the Confederates. The foundry used some of the facilities of the pre-war Augusta Arsenal, seized in January 1861. To complete the facility, the Augusta Foundry & Machine Works became a casting facility. Equipment came in from various sources. Much of it, the Confederate government purchased from civilian firms across the deep south. Augusta Foundry came on line just as many private foundries, from New Orleans, Nashville, and Memphis in particular, were overrun by the Federals. Starting in late 1862, Augusta produced a substantial number of 12-pdr Napoleons. Most of these were earmarked for the desperate Army of the Tennessee and other formations in the Western Theater. The Napoleons from Augusta matched the “Type 5? category identified by modern artillery historians. Augusta Foundry produced between 110 and 130 12-pdr Napoleon guns. Of the nearly fifty survivors, none have production dates beyond 1864. SOURCE
About the Gun
The twelve-pound cannon "Napoleon" was the most popular smoothbore cannon used during the war. It was named after Napoleon III of France and was widely admired because of its safety, reliability, and killing power, especially at close range. The Federal version of the Napoleon can be recognized by the flared front end of the barrel, called the muzzle-swell. Confederate Napoleons were produced in at least six variations, most of which had straight muzzles, but at least eight catalogued survivors of 133 identified have muzzle swells This bronze gun does not have that flare. Casting of these bronze Napoleons by the Confederacy ceased due to lack of resources and in January 1864 Tredegar began producing iron Napoleons. Just before this in early 1863, resources were so scarce, Robert E. Lee sent nearly all of the Army of Northern Virginia's bronze 6-pounder guns to Tredegar (another foundry) to be melted down and recast as Napoleons. SOURCE
About the C.S. Headquarters Markers
Foundations were built in the Autumn of 1920; through the winter of 1920-1921, the stone cutters and their helpers got out the granite for bases and dies. These bases and dies have been set up on the foundations and each monument mounted with a 12 pounder bronze Confederate gun. A bronze tablet on the die gives the necessary information, viz: The Corps Commander, the Division composing the Corps, Commander of each Division, the dates on which the Corps occupied the locality, etc. A bronze plate with C. S. A. of large letters on it is across the gun at the trunnions. The First Corps, Headquarters marker is located on Section 4, Confederate Avenue, near the Observation Tower, a bronze tablet on the base of the marker points out that the exact location was at a school-house 900 yards westerly. This school-house is in plain view from the marker and was occupied by Lieut.-General Longstreet. The Second Corps Headquarters marker is located on the north side of the Hanover road on the west side of Rock Creek 100 yards from the bridge. General Ewell occupied the house near the marker. The Third Corps Headquarters marker is located on the west side of West Confederate avenue 200 yards southerly from the McMillan woods; the tablet on the base of the marker states that the farm buildings 540 yards westerly, and in plain view, were occupied by Lieut.-General Hill during the battle. SOURCE
The inscription on the curved bronze plate reads:
Army of Northern Virginia
3rd Corps Headquarters
Lieut. General
Ambrose P. Hill
Divisions
Major Genl. R.H. Anderson
Major Genl. Henry Heth
Major Genl. William D. Pender
July 1,2,3,4. 1863
These headquarters were located at
a farm-house 540 yards westerly
The Hill's C.S. Marker - Headquarter Marker is a contributing feature to the Gettysburg National Military Park Historic District which is nationally significant under NR Criteria A, B, C & D. Areas of Significance: Military, Politics/Government, Landscape Architecture, Conservation, Archeology-Historic. Period of Significance: 1863-1938. The original National Register Nomination was approved by the Keeper March 19, 1975. An update to this nomination was approved by the Keeper on January 23, 2004. The monument is identified as structure number MN768.
From the Nomination Form:
1 of 4 Civil War C.S. Headquarters Markers of the War Dept. Era (1895-1927). Designates location of Hill's Headquarters during Battle of Gettysburg, July 1-4, 1863. Located on W side of West Confederate Avenue.
Short Physical Description:
12-pounder bronze Confederate cannon cemented into hexagonal granite base w/ muzzle up. Overall height, 10'6". 2 bronze inscription tablets on E face. Bronze plate w/ "C.S.A." inscribed, fastened across gun at trunnion.
Long Physical Description:
N/A
My Sources
1.
NRHP Nomination Form
2.
Stone Sentinels
3.
Virtual Gettysburg
4.
Draw the Sword
5.
Historical Marker Database
6.
Wikipedia