  Sazdanovic and Yip defined a categorification of Stanley's chromatic function
called the chromatic symmetric homology. In this paper we prove that (as
conjectured by Chandler, Sazdanovic, Stella and Yip), if a graph $G$ is
non-planar, then its chromatic symmetric homology in bidegree (1,0) contains
$\mathbb{Z}_2$-torsion. Our proof follows a recursive argument based on
Kuratowsky's theorem.
