One of the definitions of chase, according to Webster's, is "to pursue eagerly", so I think these qualify.
Rupert is a wild seal living in the bay, which has successfully trained humans to catch fish for it. When a boat arrives in the harbour, Rupert "pursues eagerly", to see what today's catch might bring. (Rupert is the name the local fishermen gave the seal, before they realised it's a female.)
Anyway, here's Rupert coming to see what we caught:
gratefully accepting Gerry's fish:
and "eagerly pursuing" the part of the catch the humans were intending to hang on to. :eek: