  We have discovered molecular hydrogen in a fourth quasar damped Ly-alpha
system (hereafter DLA). The UVES spectrograph on the 8.2m ESO Kueyen telescope
has allowed the detection of H2 in gas with low metallicity, Z/Z_solar ~=
10^{-2}, and high neutral hydrogen column density, N(HI) ~= 2.6*10^{21}
cm^{-2}, at redshift z_abs = 3.3901 toward QSO 0000-2620. The measured H2
fractional abundance of f(H2) ~= 4*10^{-8} is lower than a typical value for
Galactic interstellar clouds of high N(HI) column density by a factor of
(2-3)*10^6. Since H2 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(H2) value leads to an estimate of the dust number density of < n_d
>_DLA ~= 10^{-3}*< n_d >_ISM, which is consistent with the dust-to-gas ratio k
<= 1.6 10^{-3} derived independently from the [Cr/Zn] and [Fe/Zn] ratios.
