Borrowing from French chic, from German schick ("elegance, tact, style, skill"), from Middle High German schicken ("to outfit oneself, fit in, arrange appropriately"), causative of Middle High German geschehen, geschēn ("to happen, rush") from Old High German giskehan ("to happen") from Proto-Germanic *skehaną (“to run, move quickly”), from Proto-Indo-European *skek- (“to run, jump, spring”). Akin to Old English scēon ("to happen"), Dutch schielijk ("hasty").
From Wiktionary
French probably from German Schick skill, fitness, elegance from Middle High German (sich) schicken to outfit (oneself), fit in
From American Heritage Dictionary of the English Language, 5th Edition
