WordNet (r) 3.0 (2006):

chase after
    v 1: pursue someone sexually or romantically [syn: chase,
         chase after]
    2: go after with the intent to catch; "The policeman chased the
       mugger down the alley"; "the dog chased the rabbit" [syn:
       chase, chase after, trail, tail, tag, give chase,
       dog, go after, track]

Moby Thesaurus II by Grady Ward, 1.0:

19 Moby Thesaurus words for "chase after":
   bring, bring back, call for, fetch, fetch and carry, get, go after,
   go and get, go fetch, go for, go get, go to get, obtain, pick up,
   procure, retrieve, run after, secure, shag