At low redshifts, dust-obscured quasars often have strong yet narrow permitted lines in the rest-frame optical and ultraviolet, excited by the central active nucleus, earning the designation type II quasars. We present a sample of 145 candidate type II quasars at redshifts between 2 and 4.3, encompassing the epoch at which quasar activity peaked in the universe. These objects, selected from the quasar sample of the Baryon Oscillation Spectroscopic Survey of the Sloan Digital Sky Survey III, are characterized by weak continuum in the rest-frame ultraviolet (typical continuum magnitude of i~22) and strong lines of CIV and Ly{alpha}, with full width at half-maximum less than 2000km/s. The continuum magnitudes correspond to an absolute magnitude of -23 or brighter at redshift 3, too bright to be due exclusively to the host galaxies of these objects. Roughly one third of the objects are detected in the shorter wavelength bands of the Wide-Field Infrared Survey Explorer survey; the spectral energy distributions of these objects appear to be intermediate between classic type I and type II quasars seen at lower redshift. Five objects are detected at rest frame 6{mu}m by Spitzer, implying bolometric luminosities of several times 10^46^erg/s. We have obtained polarization measurements for two objects; they are roughly 3 percent polarized. We suggest that these objects are luminous quasars, with modest dust extinction (A_V_~0.5mag), whose ultraviolet continuum also includes a substantial scattering contribution. Alternatively, the line of sight to the central engines of these objects may be obscured by optically thick material whose covering fraction is less than unity.