maybe you have grassland near you. you can try to catch chickens then. they are in a flock and not as fast as rabbits.
just do it as datone said:
go next to him (leftclick on the rabbit)
-maybe click on the fastest speed you have as option- (so you'll might catch it if you were not close enough)
catch it using the RIGHTclick
in inventory: wring neck, butcher (both rightclick)
edit: datone, best you write all togher and we delete our posts then?
