Chester is only 15 miles from Tiber Dam/Lake Elwell. The lake is a popular place for summer boating, skiing, camping, swimming and fishing. During the winter ice fishing is a great way to spend a day. http://www.usbr.gov/gp/recreation/lerrec.htm
The Marias River is 20 miles south of Chester and offers a beautiful floating experience. The river winds through the Brinkman Reserve and eventually empties into the Missouri River.
Hunting, fishing and hiking is available almost anywhere in Montana and the area around Chester has great opportunities for all of the above.