Tuesday we were anchored off Matthew Town on Great Inagua near the airport and when we went to raise our anchor we found it caught on a thick cable. I dove on it and found it to be about 3″ so it is probably a communications cable because when we were on shore we noticed a BTC facility near where we were anchored. The cable is not on charts and there is no warning sign visible. When I dove on the anchor when setting it there was no sign of the cable or that we were hooking to it. The cable must be new.