Chin acne in cats is pretty common. I once had 7 cats down with it at the same time, although it is not contangious. At first we thought it was plastic food dishes and I switched to ceramic. Later the vet and I wondered if it was a new food which contained cheese and the kibbles were very oily. Mine were treated with oral antibiotics because the acne on some cats was severe and took about three weeks to clear up with both oral medication and twice-daily chin scubbing with a special vet soap. If your cat's chin doesn't have open pustules at this time, you may be able to effect a cure using the procedure Kuhio98 suggested.