This is the first time I've encountered this problem with baby chicks. We have a regular plastic waterer with the screw on bowl. I've found 2 chicks drowned in the water laying upside down in the past 2 days. I'm not sure what's going on since it's never been a problem before!
Put some pebbles or marbles in the water. They can still drink just fine, but it will not be deep enough to drown in. Sorry for your loss.