People shave their chins, rest it in all odd sorts of places, on dirty hands, and they fall down hitting their chin on the ground. Chin is a very open place and is highly vulnerable place for attacks.

And almost all these things can cause acne in the skin of your chin. Yes, it is quite possible. I used to shave with a rotary electric shaver, and I did develop symptoms of chin acne, and I immediately went ahead and looked for cures for it.