When I lived on the east side of Bozeman, this trail became my "go-to" ride, as it is close to town and affords stellar single-track riding, not to mention always supplying a great workout!
Located just outside of Bozeman, the Chestnut Mountain Trail was opened to the public in 2010 after more than a decade of hard work by the Gallatin Valley Land Trust, the Trust for Public Lands and many others. The acquisition and development of this trail is a real testament to the people who worked to make it happen and all of us owe them our appreciation for working so hard to provide new public access.
The trailhead is one of the easiest to find that you will ever visit. Exit Interstate 90 at Exit 316 (Trail Creek) which is about 8 miles east of Bozeman and 17 miles west of Livingston. At this exit you want to go south of the Interstate on Trail Creek Road. This means that if you are traveling from Bozeman you will turn right at the off ramp and if you are coming from Livingston you will turn left and drive under the Interstate.
The trailhead for Chestnut Mountain is located right on Trail Creek Road less than ¼ mile from the Interstate. The trailhead is obvious with and information sign and parking area. Although only a few cars will fit in the official parking lot there is plenty of room for vehicles along the roadside.
The Chestnut Mountain Trail is never technical, but climbs steadily for 5.3 miles to the summit, gaining 2785 ft of elevation, so the word to the wise is "conserve energy"!
From the summit you can zoom down the way you came up, or make a wonderful loop by going south from the summit, then east down to the Goose Creek trailhead and then on down Trail Creek road back to your car. Other options include veering down into the recently re-worked Bear Canyon trails to the west (spot a car at Bear Canyon trailhead), or venturing further afield across the headwaters of Bear Canyon and over the divide into the Sourdough drainage, with the fun downhill to Mystic Lake and beyond to the Sourdough trailhead (spot a car).
Here are a couple links showing these rides: