They were chasing the White Stag who gave you wishes if you caught him.
They did have dumb animals in Narnia that might rightfully be hunted - which is more unsettling than Lewis seems to have realized - to be friends with a stag, and eat his dumb likeness! Imagine being friends with a bear who was tearing into a dumb human, and offering you some.
Mrs VS
thanks for clearing that up guys...it's been a while since i've read and listened to the stories (i read TLTWATW and heard radio versions of a couple of the other stories).
And yes, VS, i see what you mean about it being unsettling.