It's genetic. His eyes aren't as red as the pic, more of a ruby, the flash brings it out.
He's what you call a brown velvet, which is another name for TOV beige. Any chinchilla with beige will have those ruby eyes. Ebony has black eyes. By breeding these two, I can get a color called tan, that looks like a dark beige, but the color shows on the belly as well as the back, like an ebony. Beige and standard (gray color you find them in in the wild) have white bellies. You add ebony, you get a colored belly, add beige, you get the red eyes. A tan will have red eyes and a colored belly.
Here's a picture of one of my trio's, there is a Standard female, a beige female, and a white male.