Observations of the QSO 0000-2620 with the Ultraviolet-Visual Echelle Spectrograph at the 8.2 m ESO Kueyen telescope are used for abundance analysis of the damped Ly alpha system at z(abs) = 3.3901. Several oxygen lines are identified in the Lya forest, and a measure for the oxygen abundance is obtained at [O/H] = -1.85 +/- 0.15 by means of the unsaturated O I lambda 925 and O I lambda 950 lines. This represents the most accurate O measurement in a damped Lya galaxy so far. We have also detected Zn II lambda 2026 and Cr II lambda lambda 2056, 2062 redshifted at approximate to 8900 Angstrom and found abundances [Zn/H] = -2.07 +/- 0.10 and [Cr/H] = - 1.99 +/- 0.09. Furthermore, previous measurements of Fe, Si, Ni, and N have been refined, yielding [Fe/H] = -2.04 +/- 0.09, [Si/H] = -1.90 +/- 0.08, [Ni/H] = -2.27 +/- 0.09, and [N/H] = -2.68 +/- 0.12. The abundance of the nonrefractory element zinc is the lowest among the damped Ly alpha systems, showing that the associated intervening galaxy is indeed in the early stages of its chemical evolution. The fact that the Zn abundance is identical to that of the refractory elements Fe and Cr suggests that dust grains have not formed yet. In this damped Lya system the observed [O, S, Si/Zn, Fe, Cr] ratios, in whatever combination are taken, are close to solar (i.e., 0.1-0.2 dex) and do not show the [alpha-element/Fe] enhancement observed in Milky Way stars of comparable metallicity. The observed behavior supports a galaxy evolution model characterized by either episodic or low star formation rate rather than a Milky Way-type evolutionary model.