We examine the spatial distribution and intrinsic properties of low-redshift (z<0.1) Ly α absorbers in HST/COS AGN spectra. Our investigation is restricted to AGN sightlines that pass through the volume mapped by Sloan Digital Sky Survey Data Release 7 (SDSS DR7). We compare the spatial distribution of Ly α absorbers to a galaxy void catalog that we generate with the VoidFinder algorithm of the Void Analysis Software Toolkit (VAST). We find that the fraction of Ly α absorbers inside voids is comparable to the volume filling fraction of voids, and much greater than the fraction of galaxies inside voids. The density of Ly α absorbers is highest near the void centers, where galaxy density is lowest, and falls off slightly near the void-wall interface. Lower column density absorbers are more centrally concentrated in voids than higher column density absorbers. We show that the spatial distributions of Ly α absorbers and galaxies inside voids differ from each other and from a random distribution to a high level of statistical significance. Our results indicate that Ly α absorbers do not trace the same large-scale structure as galaxies at low redshift. We suggest that large-scale environmental effects on the temperature and ionization fraction of the IGM cause enhanced Ly α absorption in the deep interiors of voids.