Which happened to us one night on Lake Champlain. We ended up waking up on the beach. No big deal, and we found the anchor next day(the water is so clear in that lake).
But if you're anchored in 5 or so feet, low water(like Block Island), you don't need much chain to get the rode down. Still, motor boaters can seem to be unaware of what is keeping an anchored boat, anchored.