I have several chinchilla thoughts. First of all, have you looked closely at the eyes on the black parent? Chinchilla + non-agouti self color = self chin. A self chin looks like a regular full color self, because chinchilla doesn't have any effect on self black. There's no fawn involved to get turned into pearl white. So, the black could carry chin. Self chins can have the normal brown eye, but they can also have gray, blue-gray, or marbled brown & blue, a great clue when you get it, although it makes sure you can't show the black as a full-color black, because the eye color won't be correct.
Also, full-color agouti is dominant over chin, so the agouti could have one full-color allele, and one chin hiding behind it that it could pass along. So, either of them could be carrying chin.
Secondly, my black chin kits are indeed born black. By the third day the white inside the ear really stands out, showing that it is an agouti-based color. The silvering really comes in a week or so later. The bottom photo shows one week old chinchilla kits, the one with the white inner ears is a black chin, the other is a black self chin (two chin parents, can't be a full-color self black.) The top photo shows how similar young chestnuts can look, since they also have the agouti white belly and white inner ears. Of course, once the hair starts growing, the difference will be obvious. But as newborns, you just can't tell.
The middle photo is the same black chin kit from the bottom photo, but as a three week old. (I put him and his chocolate chinchilla sister in a bowl to corral them for the photo.) You can see the silvering is definitely developing. Chinchillas that are born paler gray, not black, are going to be squirrel, blue chinchilla. The chocolate chin in the middle photo was born chocolate, and is silvering up, she'll be much lighter when she's grown. (Lilac chins are born paler pinkish-brown.)
