  The decays D^* -> D\pi and D^* -> D\gamma are well described by heavy meson
chiral perturbation theory. With the recent measurement of Br(D^{*+} -> D^+
\gamma), the D^{*0}, D^{*+}, and D_s^* branching fractions can be used to
extract the D^*D\pi and D^*D\gamma couplings $g$ and $\beta$. The D^* ->
D\gamma decays receive important corrections at order $\sqrt{m_q}$ and, from
the heavy quark magnetic moment, at order $1/m_c$. Here all the decay rates are
computed to one-loop, to first order in $m_q$ and $1/m_c$, including the effect
of heavy meson mass splittings, and the counterterms at order $m_q$. A fit to
the experimental data gives two possible solutions,
g=0.27^{+.04}_{-.02}^{+.05}_{-.02}, \beta=0.85^{+.2}_{-.1}^{+.3}_{-.1} GeV^{-1}
or g=0.76^{+.03}_{-.03}^{+.2}_{-.1}, \beta=4.90^{+.3}_{-.3}^{+5.0}_{-.7}
GeV^{-1}. The first errors are experimental, while the second are estimates of
the uncertainty induced by the counterterms. (The experimental limit
\Gamma_{D^{*+}} < 0.13 MeV excludes the $g=0.76$ solution.) Predictions for the
D^* and B^* widths are given.
