  Let $P$ be a poset, $inc(P)$ its incomparability graph, and $X_{inc(P)}$ the
corresponding chromatic symmetric function, as defined by Stanley in {\em Adv.
Math.}, {\bf 111} (1995) pp.~166--194. Certain conditions on $P$ imply that the
expansions of $X_{inc(P)}$ in standard symmetric function bases yield
coefficients which have simple combinatorial interpretations. By expressing
these coefficients as character evaluations, we extend several of these
interpretations to {\em all} posets $P$. Consequences include new combinatorial
interpretations of the permanent and other immanants of totally nonnegative
matrices, and of the sum of elementary coefficients in the Shareshian-Wachs
chromatic quasisymmetric function $X_{inc(P),q}$ when $P$ is a unit interval
order.
