From 米(kome, “rice”) + 噛み(kami, “biting, chewing”, 連用形(ren'yōkei, “stem or continuative form”) of the verb 噛む(kamu, “to bite, to chew”)), from the way one's temple moves while eating.
This etymology is missing or incomplete. Please add to it, or discuss it at the Etymology scriptorium. Particularly: “This word decomposes, most curiously, as "cricket valley". Yet it's clearly not ateji, because then it'd be read as kōrogi-tani.”