[0] From Middle English chiken (also as chike > English chick), from Old English ċicen, ċycen (“chicken”), of uncertain origin. Possibly from Proto-West Germanic kiukīn (“chicken”), or alternatively from Proto-West Germanic kukkīn, equivalent to cock + -en.
Compare North Frisian schückling (“chicken”), Saterland Frisian Sjuuken (“chicken”), Dutch kuiken (“chick, chicken”), German Low German Küken (“chick”), whence German Küken (“chick”), (elevated, obsolete) German Küchlein (“chick”) and Old Norse kjúklingr (“chicken”).
Know this song? https://www.youtube.com/watch?v=I6Yce3AxF9c
Also bonus one: https://youtu.be/miomuSGoPzI?is=IpXvzjGRIswRjUsv
Here is Die Sauerkrauts, presenting the Chicken Dance: https://youtu.be/jJcCwbV5kp8?is=Ug4EqlKjN2o9xjBe
Modern German might have changed along the way, but if you go back far enough, there should be something. I'm not a linguist or a native speaker of a Proto-Germanic language, so I don't know enough to pinpoint this better.