1 hunting, hunt, pursuit:
Police dogs entered the chase and the prisoner was finally caught.
2 run after, follow, pursue, track, go (out) after; court, woo:
The police were chasing a man down the street. Stop chasing women and settle down.
3 chase away, off, out, etc. rout, put to flight, hound; drive away, off, out, etc.:
I chased the cat away from the birdcage.