Aims. We study the dependence of galaxy clustering on luminosity and stellar mass at redshifts $z\sim$ 0.2–1, using the first 10K redshifts from the zCOSMOS spectroscopic survey of the COSMOS field.
 Methods. We measured the redshift-space correlation functions $\xi(r_{\rm p},\pi)$ and $\xi(s)$ and the projected function, $w_{\rm p}(r_{\rm p})$ for subsamples covering different luminosity, mass, and redshift ranges. We explored and quantified in detail the observational selection biases from the flux-limited nature of the survey, using ensembles of realistic semi-analytic mock samples built from the Millennium simulation. We used the same mock data sets to carefully check our covariance and error estimate techniques, comparing the performances of methods based on the scatter in the mocks and on bootstrapping schemes. We finally compared our measurements to the cosmological model predictions from the mock surveys. Results. At odds with other measurements at similar redshift and in the local Universe, we find a weak dependence of galaxy clustering on luminosity in all three redshift bins explored. A mild dependence on stellar mass is instead observed, in particular on small scales, which becomes particularly evident in the central redshift bin ($0.5<z<0.8$), where $w_{\rm p}(r_{\rm p})$ shows strong excess power on scales >1 h-1 Mpc. This is reflected in the shape of the full $\xi(r_{\rm p},\pi)$ that we interpret as produced by dominating structures almost perpendicular to the line of sight in the survey volume. Comparing to $z\sim 0$ measurements, we do not see any significant evolution with redshift of the amplitude of clustering for bright and/or massive galaxies. Conclusions. This is consistent with previous results and the standard picture in which the bias evolves more rapidly for the most massive haloes, which in turn host the highest-stellar-mass galaxies. At the same time, however, the clustering measured in the zCOSMOS 10K data at $0.5<z<1$ for galaxies with $\log(M/M_\odot)\ge 10$ is only marginally consistent with the predictions from the mock surveys. On scales larger than ~2 h-1 Mpc, the observed clustering amplitude is compatible only with ~1% of the mocks. Thus, if the power spectrum of matter is ΛCDM with standard normalisation and the bias has no “unnatural” scale-dependence, this result indicates that COSMOS has picked up a particularly rare, ~2–3σ positive fluctuation in a volume of ~106 h-1 Mpc3. These findings underline the need for larger surveys of the $z\sim 1$ Universe to appropriately characterise the level of structure at this epoch.