The purpose of this note is to prove that if A and B are unital C*-algebras and φ : A → B is a unital *-preserving ring homomorphism, then φ is contractive; i.e., ∥ φ (a) ∥ ≦ ∥ a ∥ for all a ∈ A. (Note that we do not assume φ is linear.) We use this result to deduce a number of corollaries as well as characterize the form of such unital *-preserving ring homomorphisms.