  The chromatic symmetric function $X_G$ is a power series that encodes the
proper colorings of a graph $G$ by assigning a variable to each color and a
monomial to each coloring such that the power of a variable in a monomial is
the number of times the corresponding color is used in the corresponding
coloring. The chromatic symmetric homology $H_*(G)$ is a doubly graded family
of $\mathbb{C}[\mathfrak{S}_n]$-modules that was defined by Sazdanovi\'c and
Yip (2018) as a categorification of $X_G$. Chandler, Sazdanovi\'c, Stella, and
Yip (2023) proved that $H_*(G)$ is a strictly stronger graph invariant than
$X_G$, and they also computed or conjectured formulas for it in a number of
special cases. We prove and extend some of their conjectured formulas for the
case of star graphs, where one central vertex is connected to all other
vertices and no other pairs of vertices are connected.
