UVES observations of QSO 0000-2620:: molecular hydrogen abundance in the damped Lyα system at zabs=3.3901

We have discovered molecular hydrogen in a fourth quasar damped Ly alpha system thereafter DLA). The UVES spectrograph on the 8.2m ESO Kueyen telescope has allowed the detection of H-2 in gas with low metallicity, Z/Z. similar or equal to 10(-2) and high neutral hydrogen column density, N(HI) similar or equal to 2.6 x 10(21) cm(-2), at redshift z(abs) = 3.3901 toward QSO 0000-2620. The measured H-2 fractional abundance of f(H-2) similar or equal to 4 x 10(-8) is lower than a typical value for Galactic interstellar clouds of high IV(H I) column density by a factor of (2 - 3) x 10(6). Since H-2 molecules are formed efficiently on dust grains, it implies that the dust condensation in this DLA is negligible, and hence the abundances derived from metal absorption lines are the actual ones. The obtained f(H-2) value leads to an estimate of the dust number density of [n(d)](DLA) similar to 10(-3) [n(d)](ISM), which is consistent with the dust-to-gas ratio (k) over tilde less than or equal to 1.6 x 10(-3) derived independently from the [Cr/Zn] and [Fe/Zn] ratios.