We investigate the dependence of galaxy clustering on the galaxy intrinsic luminosity at high redshift, using the data from the First Epoch VIMOS-VLT Deep Survey (VVDS). The size (6530 galaxies) and depth (I_{AB}<24) of the survey allows us to measure the projected two-point correlation function of galaxies, w_p(r_p) for a set of volume-limited samples up to an effective redshift <z>=0.9 and median absolute magnitude -19.6< M_B < -21.3. Fitting w_p(r_p) with a single power-law model for the real-space correlation function xi(r)=(r/r_0)^{-gamma}, we measure the relationship of the correlation length r_0 and the slope gamma with the sample median luminosity for the first time at such high redshift. Values from our lower-redshift samples (0.1<z<0.5) are fully consistent with the trend observed by larger local surveys. In our high redshift sample (0.5<z<1.2), we find that the clustering strength is suddenly rising around M_B^*, apparently with a sharper turn than at low redshifts. Galaxies in the faintest sample (<M_B>=-19.6) have a correlation length r_0=2.7^{+0.3}_{-0.3} h^{-1} Mpc, compared to r_0=5.0^{+1.5}_{-1.6} h^{-1} Mpc at <M_B>=-21.3. Correspondingly 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 not observed neither by large local surveys nor in our lower-redshift sample and seems to imply a significant change in the way luminous galaxies trace dark-matter halos at z~1 with respect to z~0. At our effective median redshift z~0.9 this corresponds to a strong difference of the relative bias, from b/b* < 0.7 for galaxies with L < L*, to b/b*~1.4 for galaxies with L > L*.