Using the Goddard High Resolution Spectrograph onboard the Hubble Space Telescope, we have observed Lyα absorption against stellar chromospheres along six lines of sight, with additional observations of the Mg II H and K lines along five of the lines of sight and Fe II absorption along four of the lines of sight. We found absorption near the projected velocity of the local interstellar cloud (LIC) along three lines of sight. The velocity toward the stars β Gem and σ Gem was only marginally consistent with the LIC. The single interstellar component toward 31 Com had a velocity that was inconsistent with the projected LIC velocity. Three of the lines of sight showed a multicomponent velocity structure. For the star ∊ Eri we required an additional hot, low-density component which we have interpreted as a stellar hydrogen wall. The LIC temperatures derived from our data range from 7800 to 9700 K with values of the microturbulence parameter less than 2.0 km s-1. The measured D/H ratio for the LIC along every sight line is consistent with a value of 1.6 × 10-5, the best determined value being the β Cas line of sight with D/H = 1.7 +/- 0.3 × 10-5.Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.