You have my complete sympathies. We just lost a Silkie the same way on Sat. My 6 year old was in a Spring Break camp all week, and was really looking forward to getting home to see how the baby chicks have grown. I checked on them about an hour before they got here and they were all alright. When Zach ran into the garage when he got home, he shouted out that one of them was dead. Drowned in the waterer. Very sad.
I had a regular chicken waterer than I went in to TSC one day and say that they had quail waterer bases. It was very tiny and perfect for chicks. I never had to worry about them drowning because there was not that much room just enough that they could drink.
Sorry for your poor little chick