POSSIBLE IDENTIFICATION OF A CLUSTER OF GALAXIES AT REDSHIFT Z = 3.4

We report the possible detection of a cluster of 16 radio-quiet galaxies at z = 3.4, identified in the field around the optically thick absorption system toward Q0000 - 263 at z(abs) = 3.390. Two of them, a Lyalpha emitter at z = 3.428 and the galaxy responsible for the absorption system, have redshifts spectroscopically confirmed. The other 14 galaxies identified using a multicolor imaging technique designed to detect sources in the redshift interval 3 approximately-less-than z approximately-less-than 3.5 which are characterized by a Lyman discontinuity in an otherwise flat spectrum, have broad-band spectral energy distributions identical to the two galaxies with known redshift. They are spatially distributed in two apparent clumps, around the damped absorber and the Lyalpha galaxy, respectively. A clustering analysis excludes with 98.8% confidence that this association is a realization of a Poissonian distribution and confirms that the observed clumps are real. The implications are that the 16 galaxies are members of a cluster at z almost-equal-to 3.4, by far the most distant ever detected. An estimate of the mass bounded in stars of this cluster is 3 x 10(12) M. (q0 = 0 and H0 = 50 km s-1 Mpc-1 throughout this Letter), while the total mass (baryonic + dark) is 6 x 10(14) M.. We also estimate that at z = 3.4 the correlation length is 2.2 Mpc, which, compared to the present value of 11 Mpc, suggests that the clustering evolution is still close to the linear regime.