Hike up along the Long Trail from Smugglers Notch* or drive up the Toll Road** from the Stowe Base Lodge. From the parking lot at The Nose, the final approach to The Chin is roughly a 1.25 mile scramble across the mountain's ridge rocks to the 4,395-foot high peak.
Contrary to an oft-repeated story that the mountain is named because it resembles a man's face, the fact is that the now-defunct town of Mansfield and the mountain were named for Mansfield, Connecticut, which was the home of most of the Vermont town's grantees.
*Closest access point, less than 2 miles from The Chin, but quite steep.
**As of this posting, $24 for car and up to six persons, $8 per additional person. Except for a short stretch of pavement at the bottom, it is a steep, narrow dirt road with lots of hairpins, roughly 4.1 miles to the parking lot at The Nose.