  We report the first experimental determination of the hyperfine quenching
rate of the $6s^2\ ^1\!S_0\ (F=1/2) - 6s6p\ ^3\!P_0\ (F=1/2)$ transition in
$^{171}$Yb with nuclear spin $I=1/2$. This rate determines the natural
linewidth and the Rabi frequency of the clock transition of a Yb optical
frequency standard. Our technique involves spectrally resolved fluorescence
decay measurements of the lowest lying $^3\!P_{0,1}$ levels of neutral Yb atoms
embedded in a solid Ne matrix. The solid Ne provides a simple way to trap a
large number of atoms as well as an efficient mechanism for populating
$^3\!P_0$. The decay rates in solid Ne are modified by medium effects including
the index-of-refraction dependence. We find the $^3\!P_0$ hyperfine quenching
rate to be $(4.42\pm0.35)\times10^{-2}\ \mathrm{s}^{-1}$ for free $^{171}$Yb,
which agrees with recent ab initio calculations.
