With close pairs of quasars at different redshifts, a background quasar sightline can be used to study a foreground quasar's environment in absorption. We search 149 moderate resolution background quasar spectra, from Gemini, Keck, the MMT, and the SDSS to survey Lyman Limit Systems (LLSs) and Damped Ly-alpha systems (DLAs) in the vicinity of 1.8 < z < 4.0 luminous foreground quasars. A sample of 27 new quasar-absorber pairs is uncovered with column densities, 17.2 < log (N_HI/cm^2) < 20.9, and transverse (proper) distances of 22 kpc/h < R < 1.7 Mpc/h, from the foreground quasars. If they emit isotropically, the implied ionizing photon fluxes are a factor of ~ 5-8000 times larger than the ambient extragalactic UV background over this range of distances. The observed probability of intercepting an absorber is very high for small separations: six out of eight projected sightlines with transverse separations R < 150 kpc/h have an absorber coincident with the foreground quasar, of which four have log N_HI > 10^19. The covering factor of log N_HI > 10^19 absorbers is thus ~ 50 % (4/8) on these small scales, whereas < 2% would have been expected at random. There are many cosmological applications of these new sightlines: they provide laboratories for studying fluorescent Ly-alpha recombination radiation from LLSs, constrain the environments, emission geometry, and radiative histories of quasars, and shed light on the physical nature of LLSs and DLAs.

27 pages (10 pages of figures), 5 tables, submitted to ApJ