With the exception of "chestnuts roasting on an open fire" in Nat King Cole's popular The Christmas Song, this nut is almost entirely non-existent in the average American's life. Many adults have gone their entire lives without ever even trying one. However they are much more popular in other regions of the world, such as in Europe and many Asian countries. In Japan for example, you almost never celebrate New Years without them and they are representative of mastery and strength.
There are four variations of this treenut; American, European, Chinese, and Japanese. These test results list them as being purchased in Italy. They do not disclose the species but based on popularity in that country, it is safe to assume they are referencing the European variety Castanea sativa. Furthermore, since all four of these varieties are closely related, they should have similar antioxidant content.
Chestnuts with the pellicle, which is the thin skin around the meat, test moderately high as shown in the number above. Though once the pellicle is removed, the amount of antioxidants decreases by over 80%.
Research Support, Non-U.S. Gov't: Carlsen MH, Halvorsen BL, Holte K, et al. Nutrition Journal NIH Jan 2010