[1] : WordNet (r) 2.0

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

[2] : 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

Chase >> C Words
Chase, definition of term: Chase
chase_pag1.html

After >> A Words
After, definition of term: After
after_pag1.html

Chase Away >> C Words
Chase Away, definition of term: Chase Away
chase+away_pag1.html

After Hours >> A Words
After Hours, definition of term: After Hours
after+hours_pag1.html

After All >> A Words
After All, definition of term: After All
after+all_pag1.html