We present HST/STIS observations of the optical counterpart (OT) of the gamma-ray burster GRB 000301C obtained on 2000 March 6, five days after the burst. CCD clear aperture imaging reveals a R ~ 21.50+/-0.15 source with no apparent host galaxy. An 8000 s, 1150 < lambda/A < 3300 NUV-MAMA prism spectrum shows a relatively flat continuum (in f_lambda) between 2800 and 3300 A, with a mean flux 8.7 (+0.8,-1.6)+/- 2.6 10^(-18) ergs/s/cm^2/A, and a sharp break centered at 2797+/-25 A. We interpret it as HI Lyman break at z = 2.067+/-0.025 indicating the presence of a cloud with a HI column density log(HI) > 18 on the line-of-sight to the OT. This value is conservatively a lower limit to the GRB redshift. However, the facts that large N(HI) system are usually considered as progenitors of present day galaxies and that other OTs are found associated with star forming galaxies strongly suggest that it is the GRB redshift. In any case, this represents the largest direct redshift determination of a gamma-ray burster to date. Our data are compatible with an OT spectrum represented by a power-law with an intrinsic index alpha = 1.2((f_nu propto nu^-alpha) and no extinction in the host galaxy or with alpha = 0.5 and extinction by a SMC-like dust in the OT rest-frame with A_V = 0.15. The large N(HI) and the lack of detected host is similar to the situation for damped Ly-alpha absorbers at z > 2.
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