Leaves are deciduous, simple, alternate, lanceolate, 6-10" long by 2-4" wide, dark green in the sun, lighter below, coarsely serrated with nice 1/4" long teeth and a rounded leaf base. Petioles are long, almost an inch. Lower surface can be covered with white hairs or not, do wish they would be consistent.
Flowers are monoecious, on the same inflorescence, males at the tips maturing after the females, very showy and attract lots of bees. Inflorescence can be 4-6" long with lots of flowers.
Fruit is a nut and have been eaten for ages. Like others in the Beech family (Fagaceae), the fruit is partially or totally enclosed by vegetative floral parts. In this case, they completely cover the developing fruit (2 or more) in a sharply spine covered cupule. (The oak fruit is also a nut and is only partially covered by what is commonly called the cup.)
There is a cool looking star shaped pattern formed by the vascular connections on the flat end of the fruit. The American chestnut patterns look more like a sunburst (reference, then click on the image of the fruit to see all of them).
Stems are stout, dark brown eventually, though green early in the season, with lots of lentils, lateral buds somewhat diverging from the stem. Bark has longitudinal grooves, potentially pretty deep.
As mentioned below, many chestnut plants are likely hybrids making identification difficult, but look for the long petiole, narrow and long leaf, leaf base rounded, long pointing spines on margins.
Don't be mistaken by the horse chestnuts, they are not edible. They have compound leaves.
Mt Herman Rd to the left of the Heavenly Roadside Cafe are 2 specimens.
There are at least four species of arborescent Castanea. The American chestnut C. dentata was essentially wiped out due to chestnut blight that struck the eastern mountains in New York in 1904 and by the 40's millions of trees were dead. I viewed some trees over the years at Finch Arboretum in Spokane that were planted as C. dentata. The other species include the European chestnut (C. sativa) and the Chinese Chestnut (C. mollissima).
Researchers found some American chestnuts that showed some resistance and were hybridized with the Chinese and European chestnuts and these are likely to be found North American landscapes. The Chinese chestnut introduces disease resistance and cold hardiness. In fact breeding has been going on since the late 1800's on the east coast. According to the Flora of North America, if a tree does not fit the key exactly, its likely a hybrid, and all the trees I have found do not fit as nicely as I would like.
UC Davis suggests that Chinese immigrants introduced C. mollissima in the mountains of Northern CA during the gold rush and Italians planted C. sativa along the coast of central CA. The results suggest that many trees may indeed be hybrids.
I have used almost every key I have found, and have settled on the European Chestnut. I found the American Chestnut Foundation key from the 2012 Chestnut Summit to be excellent.