My first pair had been together 6 years at their old owner's home and never mated once in the 6 years of living with her. She did leave them outside though... when they came home with me, they had their first litter five months after moving in to my home. It's what got me into raising chins, fell in love with their babies!
On the otherhand, I got a chin once some years ago, who had been passed from one breeder to another, and seemed that although he mated, he never sired a litter at any of their places.
Sure enough, I not only saw him mate, but caught the mating plug later on - and still no kits(the female he was with was a proven breeder) at my place. Kept him for three years(he was four years old when I got him) and finally found him a pet home after I had exhausted all efforts to get him to breed.
It's very rare though when you find a chinchilla like that. I got another chin from a breeder who was said to never have had babies(they were planning to pelt her, so I offered to give her a chance.), and when she came home with me, it was six or seven months later and she had her first baby. She was three years old when I got her, btw.