I wouldn't offer it. Rice is packed with carbs, which aren't necessary in the diet. The skin of the baked, grilled, bbq-ed, and fried chicken can cause major stomach upset, especially the skin. (I learned this the hard way; full day at the vet, antibiotics and an IV drip all because of chicken skin.)
Boiled chicken is fine on occasion.
Rice can be a good way to get a sickly dog or a dog without much of an appetite to eat. It's also good for dogs that are slightly dehydrated to get some moisture into the body. On the regular, though, I wouldn't recommend it.