The American chestnut is not extinct!
The term that is most applicable for the chestnut is “effectively extinct”. The American chestnut tree is threatened with extinction from blight because very few trees are producing nuts. Very few of the small sprouts will live long enough to flower, and when trees do flower, they tend to die fairly quickly. It is unclear how long it will take for most of the small sprouts to die out. In 1978 measurements, larger ones ranged in age up to 39 years old. Many are probably correspondingly older today. Our best guess is that it will take several hundred to a thousand years for American chestnut to become extinct, if it ever does.

There are few tree-sized chestnuts, but these are not exactly rare. Most sprouts are less than eight inches dbh (diameter at breast height). Because of this, you sometimes will see statements such as, “American chestnut is extinct as a large forest tree.” That statement is restricted to large forest trees, and even that is not strictly correct.

Further information can be found in the article, “Locating Flowering Trees,” in Volume 6, Number 2 of The Journal of The American Chestnut Foundation.
(http://acf.org/pdfs/resources/journal/journ_vol6-2.pdf. The entire set of back issues of the Journal is available at http://acf.org/journal.php.