  Measurements of $D^{*}(2010)$ meson production in diffractive deep inelastic
scattering $(5<Q^{2}<100~{\rm GeV}^{2})$ are presented which are based on HERA
data recorded at a centre-of-mass energy $\sqrt{s} = 319{\rm~GeV}$ with an
integrated luminosity of $287$ pb$^{-1}$ collected by the H1 detector. The
reaction $ep \rightarrow eXY$ is studied, where the system $X$, containing at
least one $D^{*}(2010)$ meson, is separated from a leading low-mass proton
dissociative system $Y$ by a large rapidity gap. The kinematics of $D^{*}$
candidates are reconstructed in the $D^{*}\rightarrow K \pi\pi$ decay channel.
The measured cross sections compare favourably with next-to-leading order QCD
predictions, where charm quarks are produced via boson-gluon fusion and they
are independently fragmented to the $D^{*}$ mesons. The calculations rely on
the collinear factorisation theorem and are based on diffractive parton
densities previously obtained by H1 from fits to inclusive diffractive cross
sections. The data are further used to determine the diffractive to inclusive
$D^{*}$ production ratio in deep inelastic scattering.
