  We describe a first measurement of the radiation from a $^{\bf 178m}$Hf
sample to search for dark matter. The $\gamma$ flux from this sample, possessed
by Los Alamos National Laboratory nuclear chemistry, was measured with a Ge
detector at a distance of 4 ft due to its high activity. We search for
$\gamma$s that cannot arise from the radioactive decay of $^{\bf 178m}$Hf, but
might arise from the production of a nuclear state due to the inelastic
scattering with dark matter. The limits obtained on this $\gamma$ flux are then
translated into constraints on the parameter space of inelastic dark matter.
Finally, we describe the potential reach of future studies with $^{\bf
178m}$Hf.
