I have the same problem. I have PolyCystic Ovary Syndrome. One of the symptomes is excess growth of hair. >.< Yes its something that Im ashamed of but its true and I hate it. But I was told there is a cream out there to take care of it, it was just like 100 dollars so I couldnt afford it. But go to your OBGYN and ask them or a Dermatologist..
Meet a dermatologist and get this examined, you will also need to do hormonal tests to see that it is not caused due to male hormones in your body, in that case the treatment will vary otherwise you can do laser removal of the chin hairs i guess.