I actually don't have a top for my current chick feeder (it's one of those round plastic bases meant to screw onto a mason jar) but it's so shallow that the chicks can climb into and out of it if they want.and a word of advice: don't get the feeders and waterers without lids. I've never had a drowning from falling in, but I had an idiot who died presumably of thirst after falling into the feeder
I could see a chick maybe getting into more trouble with a larger adult feeder, if they somehow fell into the top, though doing regular headcounts of chicks would probably be the best counter to that.