Observations of the QSO 0000–2620 with UVES spectrograph at the 8.2m 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 Ly \alpha forest and a measure for the oxygen abundance is obtained at [ O/H ] =–1.85 \pm 0.1 by means of the unsaturated OI \lambda 925Å and OI \lambda 950Å lines . This represents the most accurate O measurement in a damped Ly \alpha galaxy so far . We have also detected ZnII \lambda 2026 Å and CrII \lambda 2056 , \lambda 2062 Å redshifted at \approx 8900 Å and found abundances [ Zn/H ] = –2.07 \pm 0.1 and [ Cr/H ] =–1.99 \pm 0.1 . Furthermore , previous measurements of Fe , Si , Ni and N have been refined yielding [ Fe/H ] =–2.04 \pm 0.1 , [ Si/H ] =–1.90 \pm 0.1 , [ Ni/H ] =–2.27 \pm 0.1 , and [ N/H ] =–2.68 \pm 0.1 . The abundance of the non-refractory 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 Ly \alpha 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 .