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