The first HST GHRS spectra of the bright BL Lacertae object PKS 2155-304, acquired using the G140L configuration, show a smooth, featureless continuum with superposed sharp absorption. This absorption is due to both gas in the Galactic halo above the south Galactic pole and what are identified as five to six low redshift Lyalpha absorption systems arising in the local intergalactic medium. Complex absorption features of C IV indicate highly ionized gas at near zero velocity and almost-equal-to -260 km s-1 falling toward the Galactic plane. The identified Lyalpha systems cover a range of redshift 0.057 less-than-or-equal-to z less-than-or-equal-to 0.107. These observations confirm two features and rule out two others that were previously identified in summed IUE spectra of PKS 2155-304. The GHRS data resolve the strongest Lyalpha feature previously detected in the IUE data into three distinct components within the interval z = 0.055-0.057. A galaxy within 14' in the plane of the sky to PKS 2155 - 304 with the same measured redshift as that of inferred Lyalpha absorption at z almost-equal-to 0.017 may indicate that this gas is associated with a galaxy cluster. The highest redshift observed Lyalpha system provides a lower limit to the distance of the BL Lacertae object (z > 0.105). This distance is consistent with the approximate redshift deduced from CCD imagery of the probable host galaxy for PKS 2155 - 304 (z approximately 0. 1 2). The Lyalpha systems seen toward PKS 2155-304 are compared to those in the line of sight to 3C 273. A two-point correlation analysis shows no statistical evidence of clustering of Lyalpha features. However, apparent redshift correlations with galaxies along the line of sight argue that some significant fraction of the observed Lyalpha systems are associated with galaxies or galaxy clusters.