Godan verb with 'u' ending, Intransitive verb
to flatter; to curry favour (with); to play up (to); to toady (to); to fawn (on)
こびへつらうウェイターは最上のテーブルをあてがわれる。なぜなら、そうしたウェイターは、いつもマネージャーや上役のきげんをとるから。The obsequious waiter is usually assigned the best table because he always curries favor with his manager and superiors.
Also written 媚び諂う【こびへつらう】