  A search for associated production of a $Z$ boson with an open charm meson is
presented using a data sample, corresponding to an integrated luminosity of
$1.0\,\mathrm{fb}^{-`}$ of proton--proton collisions at a centre-of-mass energy
of 7\,TeV, collected by the LHCb experiment. %% Seven candidate events for
associated production of a $Z$ boson with a $D^0$ meson and four candidate
events for a $Z$ boson with a $D^+$ meson are observed with a combined
significance of 5.1standard deviations. The production cross-sections in the
forward region are measured to be $$\sigma_{Z\rightarrow\mu^+\mu^-\!,D^0} =
2.50\pm1.12\pm0.22pb$$ $$\sigma_{Z\rightarrow\mu^+\mu^-\!,D^+} =
0.44\pm0.23\pm0.03pb,$$ where the first uncertainty is statistical and the
second systematic.
