We present HST /STIS observations of the optical counterpart ( OT ) of the \gamma -ray burster ( catalog GRB~000301C ) obtained on 2000 March 6 , five days after the burst . CCD clear aperture imaging reveals a R \simeq 21.50 \pm 0.15 source with no apparent host galaxy . An 8000 s , 1150 < \lambda / \mbox { \AA } < 3300 NUV–MAMA prism spectrum shows a flat or slightly rising continuum ( in f _ { \lambda } ) between 2800 and 3300 Å , with a mean flux 8.7 ^ { +0.8 } _ { -1.6 } \pm 2.6 ~ { } 10 ^ { -18 } ~ { } \mathrm { ergs } ~ { } \mathrm { s } ^ { -1 } ~ { } % \mathrm { cm } ^ { -2 } ~ { } \mbox { \AA } ^ { -1 } , and a sharp break centered at 2797 \pm 25 Å . We interpret this as the H i Lyman break at z = 2.067 \pm 0.025 indicating the presence of a cloud with a H i column density \log { ( N _ { \mathrm { HI } } ~ { } \mathrm { cm } ^ { 2 } ) } > 18 on the line-of-sight to the OT . This measured redshift is conservatively a lower limit to the GRB redshift . However , as all other GRBs which have deep HST images appear to lie on the stellar field of a host galaxy , and as the large H i column density measured here and in later ground-based observations is unlikely on a random line-of-sight , we believe we are probably seeing absorption from H i in the host galaxy . 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 SMC-like dust in the OT rest-frame with A _ { \mathrm { V } } = 0.15 . The large N _ { \mathrm { HI } } and the lack of a detected host are similar to the situation for damped Ly- \alpha absorbers at z > 2 .