Call customer service. Is it gold? Sterling silver? Are you missing pieces of the chain? It probably will not cost you more than $20 if you have all of the pieces.
My mom and I both had necklaces break just recently. My mom's was a gold necklace w/ pendant and my mind was a sterling silver necklace with pendant. We both had our pieces for a few years now. We just took them into our local Tiffany and they fixed both of our necklaces for free.
Give them a call before you do it and they'll tell you the price. I just called them because the clasp on a bracelet was broken, and I think they said that would be $35. A broken chain should be less.