I use those plastic packing box lids to feed the chickens on.
For Dark Cornish Mama and her crew, I place chick starter on the uphill end. Water is gently poured onto the downhill end. The babies could dance in the water and it wouldn't come up to their little knees!
I, too, have been worried about chicks falling into a drink container and drowning. So far that has been avoided around here. I would have sworn that my adult hens were trying to fall through the ice this past Winter. Stand on the ice and drink through the hole I had broke. Arrgh! Anyway, to protect the stupid I switched to more shallow containers. The only reedeming quaility to using a large washtub forthe hens is: when full of water, all the girls can perch on the side and drink without flipping it over. When the water gets low, they stand in the water up to their tail feathers to drink. I guess they are "cooling it", lol.