  We present a galaxy group catalogue spanning the redshift range 0.1 <~ z <~ 1
in the ~1.7 deg^2 COSMOS field, based on the first ~10,000 zCOSMOS spectra. The
performance of both the Friends-of-Friends (FOF) and Voronoi-Delaunay-Method
(VDM) approaches to group identification has been extensively explored and
compared using realistic mock catalogues. We find that the performance improves
substantially if groups are found by progressively optimizing the group-finding
parameters for successively smaller groups, and that the highest fidelity
catalogue, in terms of completeness and purity, is obtained by combining the
independently created FOF and VDM catalogues. The final completeness and purity
of this catalogue, both in terms of the groups and of individual members,
compares favorably with recent results in the literature. The current group
catalogue contains 102 groups with N >= 5 spectroscopically confirmed members,
with a further ~700 groups with 2 <= N <= 4. Most of the groups can be assigned
a velocity dispersion and a dark-matter mass derived from the mock catalogues,
with quantifiable uncertainties. The fraction of zCOSMOS galaxies in groups is
about 25% at low redshift and decreases toward ~15% at z ~ 0.8. The zCOSMOS
group catalogue is broadly consistent with that expected from the semi-analytic
evolution model underlying the mock catalogues. Not least, we show that the
number density of groups with a given intrinsic richness increases from
redshift z ~ 0.8 to the present, consistent with the hierarchical growth of
structure.
