A measurement is presented of the cross section for D*+/- meson production
in diffractive deep-inelastic scattering for the first time at HERA. The cr
oss section is given for the process ep --> eXY, where the system X contain
s at least one D*+/- meson and is separated by a large rapidity gap from a
low mass proton remnant system Y. The cross section is presented in the dif
fractive deep-inelastic region defined by 2 < Q(2) < 100 GeV2, 0.05 < y < 0
.7, x(P) < 0.04, M-Y < 1.6 GeV and \t \ < 1 GeV2. The D*+/- mesons are rest
ricted to the range P-T,P-D* > 2 GeV and \ eta (D*)\ < 1.5. The cross secti
on is found to be 246 +/- 54 +/- 56 ph and forms about 6% of the correspond
ing inclusive D*+/- cross section. The cross section is presented as a func
tion of various kinematic variables, including z(P)(obs) which is an estima
te of the fraction of the momentum of the diffractive exchange carried by t
he parton entering the hard-subprocess. The data show a large component of
the cross section at low Z(obs)(P) where the contribution of the boson-gluo
n-fusion process is expected to dominate. The data are compared with severa
l QCD-based calculations. (C) 2001 Elsevier Science B.V. All rights reserve
d.