One option is to strategically plan out empty events at the corners and places that it gets easily stuck at. Given that the chicken does not have 'through' enabled, it will not pass through empty events (even though the player still can). That way, it's somewhat of an invisible bouncy barrier to avoid it running into a dead end.
Another alternative choice would be to manually set its movement pattern. This might take some time, but can be effective if planned out carefully knowing where the player starts out. Perhaps have it run in circles, and if you wanna get fancy set some conditional branches such that if player's map coordinate = below it (use variables), move one route instead of the other. Etc. Might be too complicated though, so I suggest just try out the invisible barrier thing.