  Joret, Micek, Milans, Trotter, Walczak, and Wang recently asked if there
exists a constant $d$ such that if $P$ is a poset with cover graph of $P$ of
pathwidth at most $2$, then $\dim(P)\leq d$. We answer this question in the
affirmative by showing that $d=17$ is sufficient. We also show that if $P$ is a
poset containing the standard example $S_5$ as a subposet, then the cover graph
of $P$ has treewidth at least $3$.
