  Stanley associated with a graph G a symmetric function X_G which reduces to
G's chromatic polynomial under a certain specialization of variables. He then
proved various theorems generalizing results about the chromatic polynomial, as
well as new ones that cannot be interpreted at that level. Unfortunately, X_G
does not satisfy a Deletion-Contraction Law which makes it difficult to apply
induction. We introduce a symmetric function in noncommuting variables which
does have such a law and specializes to X_G when the variables are allowed to
commute. This permits us to further generalize some of Stanley's theorems and
prove them in a uniform and straightforward manner. Furthermore, we make some
progress on the (3+1)-free Conjecture of Stanley and Stembridge.
