  A precision measurement of the mass difference between the $D^0$ and $D^{*0}$
mesons has been made using 316~pb$^{-1}$ of $e^{+}e^{-}$ annihilation data
taken at $\sqrt{s}=4170$~MeV using the CLEO-c detector. We obtain $\Delta M
\equiv M(D^{*0})-M(D^0) =142.007\pm0.015$(stat)~$\pm$~0.014(syst)~MeV, as the
average for the two decays, $D^0\to K^-\pi^+$ and $D^0\to K^-\pi^+\pi^-\pi^+$.
The new measurement of $\Delta M$ leads to $M(D^{*0})=2006.850\pm0.049$~MeV,
and the currently most precise measurement of the binding energy of the
``exotic'' meson X(3872) if interpreted as a $D^0D^{*0}$ hadronic molecule,
$E_{b}(\text{X}(3872))\equiv M(D^0D^{*0})-M(\text{X}(3872))=3\pm192$ keV.
