  The oriented chromatic number of a directed graph $G$ is the minimum order of
an oriented graph to which $G$ has a homomorphism. The oriented chromatic
number $\chi_o({\cal F})$ of a graph family ${\cal F}$ is the maximum oriented
chromatic number over any orientation of any graph in ${\cal F}$. For the
family of hexagonal grids ${\cal H}_2$, Bielak (2006) proved that $5 \le
\chi_o({\cal H}_2) \le 6$. Here we close the gap by showing that $\chi_o({\cal
H}_2) \ge 6$.
