  We study the novel decays $B^{*}\to B\gamma\gamma $ and $D^{*}\to D\gamma
\gamma $ using the framework of the Heavy Meson Chiral Lagrangian (HM$\chi$L)
to leading order in chiral perturbation theory. The branching ratios of these
decays are expressed in terms of the strong $g_{B^{*}(D^{*})B(D)\pi}$ and the
electromagnetic $g_{B^{*}(D^*)B(D)\gamma}$ couplings, thus providing a possible
tool for their determination. In the charm case, using the experimentally
determined ratios $({D^*}^{0,+}\to D\pi)/({D^*}^{0,+}\to D\gamma),$ we are able
to express the branching ratio as a function of the strong coupling only. We
thus find $1.6\times 10^{-6}<{\rm Br} ({D^{*}}^{0}\to
D^0\gamma\gamma)<3.3\times 10^{-5}$ for $0.25<g<1,$ where $g$ is the strong
coupling of HM$\chi$L. In the beauty sector, the ${\rm Br}({B^{*}}^{0} \to B^0
\gamma\gamma)$ which we estimate to be in the $10^{-7}-10^{-5}$ range is a
function of both $g_{B^{*}B\pi}$ and $g_{B^{*}B\gamma}.$ Its behaviour does not
afford an unambiguous determination of these couplings except for the region of
high $g$ values like $g>0.6.$ The expected two-photon differential
distributions are presented for both ${B^{*}}^{0} \to B^0 \gamma\gamma$ and
${D^{*}}^{0}\to D^0\gamma\gamma,$ for different values of the couplings
involved.
