Question
While in West Virginia I saw a tree which had hard round spikey green balls (for lack of a better word) hanging from it.  The spikes were very sharp and when they fell to the ground they turned brown with age.  We tried to open one but it was very hard and had a nut inside that looked something like a hazelnut.  What kind of tree is this?

Answer
Sounds like one of the chestnuts.
Chestnut is a common name for several species of trees in the genus Castanea, in the Beech family Fagaceae. Chestnuts are native to warm temperate regions of the Northern Hemisphere. The name also refers to the edible nuts produced by these trees. Most are large trees to 20-40 m tall, but some species are smaller, often shrubby. All are flowering broadleafs with catkins.

The fruit is a spiny cupule 5-11 cm diameter, containing one to seven nuts. Most of the American Chestnuts were killed by a blight many years ago but there are some survivers in the wild forests.
Once an important hardwood timber tree, American Chestnut is highly susceptible to chestnut blight, caused by an Asian bark fungus (Cryphonectria parasitica, formerly Endothia parasitica) accidentally introduced to America on imported Asiatic chestnut trees. The disease was first noticed on American Chestnut trees in the Bronx Zoo in 1904. While Chinese Chestnuts evolved with the blight and are usually immune, the airborne bark fungus spread 50 miles a year and in a few decades girdled and killed billions of American Chestnuts. New shoots often sprout from the roots when the main stem dies, so the species has not yet become extinct. However, the stump sprouts rarely reach more than 6 meters (20 ft) in height before blight infection returns.


Young tree in natural habitat It is estimated that the total number of chestnut trees in eastern North America was over 3 billion, and that 25 percent of the trees in the Appalachian Mountains were American Chestnut. The number of large surviving American Chestnut trees over 60 cm (24 inches) in diameter within the tree's former range is probably less than 100.


If the tree was in a more urban setting I would guess it to be Chinese Chestnut.

Here is a web link to Chinese chestnut and American Chestnut. At the bottom of the web page is another link to each tree information
http://www.cnr.vt.edu/dendro/comparison/