We present the earliest ever ultraviolet spectrum of a gamma-ray burst (GRB) as observed with the Swift-UVOT. The GRB 081203A spectrum was observed for 50 seconds with the UV grism starting 251 seconds after the Swift-BAT trigger when the GRB was of
u ~13.4 mag and still rising to its peak optical brightness. The UV grism spectrum shows a damped Ly-alpha line, Ly-beta, and the Lyman continuum break at a redshift z = 2.05 +/- 0.01. A model fit to the Lyman absorption implies log N(HI) = 22.0 +/- 0.2 cm-2, which is typical for GRB host galaxies with damped Ly-alpha absorbers. This observation of GRB 081203A demonstrates that for GRBs brighter than v ~14 mag and with 0.5 < z < 3.5 the UVOT will be able to provide redshifts, and probe for damped Ly-alpha absorbers within 4-6 minutes from the time of the Swift-BAT trigger.
