Chin acne is usually caused by oils in the food and bacteria.  It is not generally serious if you catch it early and treat it.  If it gets bad, it can become very problematic, with infection.  If the kitty eats out of a plastic bowl, try switching to a ceramic, glass, or metal one—and make sure you wash it out every day (put the dry food that is left over in another container while you wash and thoroughly dry it, then put back in bowl).   Plastic, no matter how well you try and take care of it, will always harbor some bacteria.  Also, make sure you are feeding a high quality dry diet (if you feed dry at all)--cheaper foods often exacerbate this problem because of ingredient choices. 

To treat the skin, I usually wash the chin with warm water and a wash cloth, using gentle pressure and a circular motion.  You need to thoroughly clean the area, but try not to irritate it—that will make it worse.  I do that a couple times a day.  If your kitty is particularly good about baths and face washing, I like to dilute a little plain Dawn or Ivory dish soap and then make a little lather on a wash cloth and clean with that.  However, you need to rinse the heck out of that, or it will irritate and make it worse--so I recommend that only with kitties who are comfortable with water around the face.  After the area is clean there are a couple things to try—hydrogen peroxide on a cotton pad—wet the area, also 2-3 times a day.  Try not to get it in the mouth—yuck.  If that doesn’t work after a few days, try Neosporin ointment, just make sure it is the plain kind—NOT the one with the painkiller in it—that is poison to cats!  Or you can get the benzyl peroxide pads in a jar for teen acne, and gently cleanse the area with those.  Again, try and keep it out of the mouth/off the lips/not touching the nose (they burn). Look for the ones with the lowest concentration of ingredient, if they have one for sensitive skin, that usually is better, too, because it shouldn’t be fragranced and have tons of alcohol in it.