Wiktionary [0] seems pretty confident ("Germanic" includes all of the languages below, not just modern German).

[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”).