DAMPED Lyman-alpha systems are high column-density intergalactic clouds of hydrogen, the existence of which is inferred from absorption lines appearing in the emission spectra of distant quasars. The galaxies believed to be responsible for these absorption systems have been suggested as possible progenitors of the normal disk galaxies observed in the local Universe(1). Indeed, Lyman-alpha systems appear to contain a substantial fraction of the baryons known to exist in galaxies today(2,3). Here we report the optical detection of a galaxy (designated DLA2233 + 131) associated with a known(4) damped Lyman-alpha absorption system at a redshift of z = 3.150. The properties of this galaxy correspond closely to those expected of a young disk galaxy in the early stages of formation, and show no evidence for an active nucleus. This finding gives strong support to the idea that damped Lyman-alpha systems represent a population of young galaxies at high redshifts.