Most villas have them and they normally provided by the management company. Check with your agency. That's one of the things I check when we check in. I like a chair on the beach!
I don't know why, but we never used beach chairs during first four trips to St John, even though every villa had them. We decided to give them a try on our fifth trip and now I have to have them! I much prefer sitting on a beach chair to sitting on a towel.