  The chromatic symmetric function $X_G$ of a graph $G$ was introduced by
Stanley. In this paper we introduce a quasisymmetric generalization $X^k_G$
called the $k$-chromatic quasisymmetric function of $G$ and show that it is
positive in the fundamental basis for the quasisymmetric functions. Following
the specialization of $X_G$ to $\chi_G(\lambda)$, the chromatic polynomial, we
also define a generalization $\chi^k_G(\lambda)$ and show that evaluations of
this polynomial for negative values generalize a theorem of Stanley relating
acyclic orientations to the chromatic polynomial.
