I buy these every year for soup; they keep more than a month, perhaps even two months. I've had an open jar in there for about a month now and they are fine. See recipe kindly posted by Gio on this thread:
Aimee I take it back! I just checked the jar in my frig and found that a couple of the chestnuts are beginning to grow mold. I threw those out and froze the rest. So I would keep no longer than one month.