I'm having the same problem with the sewing part for my caviar classic, but on the strap!! the bag is 4-months old!!!!!!!!! It's the part where a thread binds the leather strap together... AND IT'S BROKEN
I bought it at saks in NY but now I am in Dallas so took it to their only Chanel boutique here and they are giving me such a hard time because I don't have a PHYSICAL receipt. I have a picture of the original receipt and the tag that matches everything on the receipt
Hope you have a better luck! Try taking it to the store/boutique anyway and see if they can fix it. It's definitely worth trying! Good luck!