  Let $G$ be a simple graph on $d$ vertices. We define a monomial ideal $K$ in
the Stanley-Reisner ring $A$ of the order complex of the Boolean algebra on $d$
atoms. The monomials in $K$ are in one-to-one correspondence with the proper
colorings of $G$. In particular, the Hilbert polynomial of $K$ equals the
chromatic polynomial of $G$.
  The ideal $K$ is generated by square-free monomials, so $A/K$ is the
Stanley-Reisner ring of a simplicial complex $C$. The $h$-vector of $C$ is a
certain transformation of the tail $T(n)= n^d-k(n)$ of the chromatic polynomial
$k$ of $G$. The combinatorial structure of the complex $C$ is described
explicitly and it is shown that the Euler characteristic of $C$ equals the
number of acyclic orientations of $G$.
