We have investigated the dependence of galaxy clustering on their intrinsic luminosities at z ~ 1, using the data from the First Epoch VIMOS-VLT Deep Survey (VVDS). We have measured the projected two-point correlation function of galaxies, w_p(r_p), for a set of volume-limited samples at an effective redshift =0.9 and median absolute magnitude -19.6< M_B < -21.3. We find that the clustering strength is rising around M_B^*, apparently with a sharper turn than observed at low redshifts. The slope of the correlation function is observed to steepen significantly from \gamma=1.6^{+0.1}_{-0.1} to \gamma=2.4^{+0.4}_{-0.2}. This is due to a significant change in the shape of w_p(r_p), increasingly deviating from a power-law for the most luminous samples, with a strong upturn at small (< 1-2 h^{-1} Mpc) scales. This trend, not observed locally, also results in a strong scale dependence of the relative bias, b/b* and possibly imply a significant change in the way luminous galaxies trace dark-matter halos at z ~ 1 with respect to z ~ 0
