Deodorant is fine to use on any body part that will not become irritated.

Do not use it on mucous membranes (nose, throat, genitals, etc.) But on normal skin, no problem.

Antiperspirants are a different story. You should limit the areas you use these on. They actually prevent the perspiration glands from working. Under certain circumstances, this could be dangerous. Sweat is the body's way of cooling off. If you prevent that in too many spots, your body will overheat. The chest is one area responsible for cooling the upper body and upper extremities as well as the armpits - you must allow something to sweat! Stick to using antiperspirants on your armpits if at all. Some researchers are finding that the use of antiperspirants in athletic situations can be harmful.