Is it safe to feed some of the leftover chicken to out pet Chihuahua?

As long as you haven't added a great deal of salt or powdered stock to the broth you're cooking in, it's absolutely fine - a lot of breeders and vets (myself included) believe a natural diet is far healthier for dogs than manufactured dog foods, anyway. Just don't give him chicken with any bones in, as they can splinter easily and damage his internal system.