  We prove a new signed elementary symmetric function expansion of the
chromatic quasisymmetric function of any natural unit interval graph. We then
use a sign-reversing involution to prove a new combinatorial formula for
K-chains, which are graphs formed by joining cliques at single vertices. This
formula immediately implies $e$-positivity and $e$-unimodality for K-chains. We
also prove a version of our signed $e$-expansion for arbitrary graphs.
