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We present photometry and spectroscopy of the afterglow of GRB 030323. VLT spectra of the afterglow show damped Lyalpha (DLA) absorption and low- and high-ionization lines at a redshift z=3.3718B10.0005. The inferred neutral hydrogen column density, log N(H I)=21.90B10.07, is larger than any (GRB- or QSO-) DLA H I column density inferred directly from Lyalpha in absorption. From the afterglow photometry, we derive a conservative upper limit to the host-galaxy extinction: AV<0.5 mag. The iron abundance is [Fe/H]=-1.47B10.11, while the metallicity of the gas as measured from sulphur is [S/H]=-1.26B10.20. We derive an upper limit on the H2 molecular fraction of 2N(H2)/(2N(H2)+ N(H I))b 210-6. In the Lyalpha trough, a Lyalpha emission line is detected, which corresponds to a star-formation rate (not corrected for dust extinction) of roughly 1 Mb yr-1. All these results are consistent with the host galaxy of GRB 030323 consisting of a low metallicity gas with a low dust content. We detect fine-structure lines of silicon, Si II*, which have never been clearly detected in QSO-DLAs; this suggests that these lines are produced in the vicinity of the GRB explosion site. Under the assumption that these fine-structure levels are populated by particle collisions, we estimate the H I volume density to be nH I=102-104 cm-3. HST/ACS imaging 4 months after the burst shows an extended AB(F606W)=28.0B10.3 mag object at a distance of 0. ''14 (1 kpc) from the early afterglow location, which presumably is the host galaxy of GRB 030323. Based on observations collected at the European Southern Observatory, Chile, by GRACE (Gamma-Ray Burst Afterglow Collaboration at ESO), under program ID 70.D-0523(B), and with NASA's Hubble Space Telescope

The host of GRB 030323 at $\mathsf{\textit{z}=3.372}$: A very high column density DLA system with a low metallicity