  We measure hyperfine structure in the metastable ${^3P}_2$ state of
$^{173}$Yb and extract the nuclear magnetic octupole moment. We populate the
state using dipole-allowed transitions through the ${^3P}_1$ and ${^3S}_1$
states. We measure frequencies of hyperfine transitions of the ${^3P}_2
\rightarrow {^3S}_1$ line at 770 nm using a Rb-stabilized ring cavity resonator
with a precision of 200 kHz. Second-order corrections due to perturbations from
the nearby ${^3P}_1$ and ${^1P}_1$ states are below 30 kHz. We obtain the
hyperfine coefficients as: $A=-742.11(2)$ MHz, $B=1339.2(2)$ MHz, which
represent two orders-of-magnitude improvement in precision, and $C=0.54(2)$
MHz. From atomic structure calculations, we obtain the nuclear moments:
quadrupole $Q=2.46(12)$ b and octupole $\Omega=-34.4(21)$ b\,$\times \mu_N$.
