We present preliminary results of an ESO-VLT large programme (AMAZE)aimed at determining the evolution of the mass-metallicity relation atz~3 by means of deep near-IR spectroscopy. Gas metallicities and stellarmasses are measured for an initial sample of nine star forming galaxiesat z~3.3. When compared with previous surveys, the mass-metallicityrelation inferred at z~3.3 shows an evolution significantly strongerthan observed at lower redshifts. There are also some indications thatthe metallicity evolution of low mass galaxies is stronger relative tohigh mass systems, an effect which can be considered as the chemicalversion of the galaxy downsizing. The mass-metallicity relation observedat z~3.3 is difficult to reconcile with the predictions of somehierarchical evolutionary models. We shortly discuss the possibleimplications of such discrepancies.