A Chestnut Tree! They can be identified by their long, lance-shaped leaves with the doubly sharp tips and pointed ends. Normally these a smaller shrubs mixed in with larger beech, birch, hickory, oak and maple trees. They normally don't get to be tree-sized because they are attacked by a blight destroys their bark and kills the tree. The sapplings keep re-sprouting from the old roots.
There was a 6" diameter American Chestnut growing along the side of the RecPath in the City R.O.W. that was about 30' tall and was dropping the nuts. The bark was smooth and grey, like a beech tree, but there was no sign of fissures or blight in the bark. Normally the blight hits the sapplings way before they get this big and start producing nuts.
These trees were wiped out in most of the East Coast in the early 1910's by an imported fungus. The American Chestnut were massive trees and one of the most valuable trees in the forest both for its nuts and it's lumber. Many people have been trying to restore disease-resistant hybrids for years. The Connecticut Agricultural Experiment Station has had a cross-breeding program going on for decades.
So maybe this is a lucky survivor that hasn't gotten the blight yet, or it's a disease resistant decedent, in which case it should be observed and protected. Lets hope it continues in good health. Remember to look around when you're out hiking; some times it pays to see the trees that make up the forest.