We report on observations of a Type II quasar at redshift z = 3.288 , identified as a hard X-ray source in a 185 ks observation with the Chandra X-ray Observatory and as a high-redshift photometric candidate from deep , multiband optical imaging . CXO J084837.9+445352 ( hereinafter CXO52 ) shows an unusually hard X-ray spectrum from which we infer an absorbing column density N _ { H } = ( 4.8 \pm 2.1 ) \times 10 ^ { 23 } cm ^ { -2 } ( 90 % confidence ) and an implied unabsorbed 2 - 10 keV rest-frame luminosity of L _ { 2 - 10 } = 3.3 \times 10 ^ { 44 } { ergs s ^ { -1 } } , well within the quasar regime . Hubble Space Telescope imaging shows CXO52 to be elongated with slight morphological differences between the WFPC2 F814W and NICMOS F160W bands . Optical and near-infrared spectroscopy of CXO52 show high-ionization emission lines with velocity widths \sim 1000 { km s ^ { -1 } } and flux ratios similar to a Seyfert 2 galaxy or radio galaxy . The latter are the only class of high-redshift Type II luminous AGN which have been extensively studied to date . Unlike radio galaxies , however , CXO52 is radio quiet , remaining undetected at radio wavelengths to fairly deep limits , f _ { 4.8 GHz } < 40 \mu Jy . High-redshift Type II quasars , expected from unification models of active galaxies and long-thought necessary to explain the X-ray background , are poorly constrained observationally with few such systems known . We discuss recent observations of similar Type II quasars and detail search techniques for such systems : namely ( 1 ) X-ray selection , ( 2 ) radio selection , ( 3 ) multi-color imaging selection , and ( 4 ) narrow-band imaging selection . Such studies are likely to begin identifying luminous , high-redshift Type II systems in large numbers . We discuss the prospects for these studies and their implications to our understanding of the X-ray background .