  The complex optical properties of a single crystal of hexagonal FeCrAs ($T_N
\simeq 125$ K) have been determined above and below $T_N$ over a wide frequency
range in the planes (along the $b$ axis), and along the perpendicular ($c$
axis) direction. At room temperature, the optical conductivity
$\sigma_1(\omega)$ has an anisotropic metallic character. The electronic band
structure reveals two bands crossing the Fermi level, allowing the optical
properties to be described by two free-carrier (Drude) contributions consisting
of a strong, broad component and a weak, narrow term that describes the
increase in $\sigma_1(\omega)$ below $\simeq 15$ meV. The dc-resistivity of
FeCrAs is ``non-metallic'', meaning that it rises in power-law fashion with
decreasing temperature, without any signature of a transport gap. In the
analysis of the optical conductivity, the scattering rates for both Drude
contributions track the dc-resistivity quite well, leading us to conclude that
the non-metallic resistivity of FeCrAs is primarily due to a scattering rate
that increases with decreasing temperature, rather than the loss of free
carriers. The power law $\sigma_1(\omega) \propto \omega^{-0.6}$ is observed in
the near-infrared region and as $T\rightarrow T_N$ spectral weight is
transferred from low to high energy ($\gtrsim 0.6$ eV); these effects may be
explained by either the two-Drude model or Hund's coupling. We also find that a
low-frequency in-plane phonon mode decreases in frequency for $T < T_N$,
suggesting the possibility of spin-phonon coupling.
