Chasing each other merrily.
Tennyson.
Chase, v. i. To give chase; to hunt; as, to chase around after a doctor. [Colloq.]
Chase, n. [Cf. F. chasse, fr. chasser. See Chase, v.] 1. Vehement pursuit for the purpose of killing or capturing, as of an enemy, or game; an earnest seeking after any object greatly desired; the act or habit of hunting; a hunt. "This mad chase of fame." Dryden.
You see this chase is hotly followed.
Shak.