We detect the large-scale structure of Ly \alpha emission in the Universe at redshifts z = 2 - 3.5 by measuring the cross-correlation of Ly \alpha surface brightness with quasars in the Sloan Digital Sky Survey ( SDSS/BOSS ) . We use nearly a million spectra targeting Luminous Red Galaxies ( LRGs ) at z < 0.8 , after subtracting a best fit model galaxy spectrum from each one , as an estimate of the high-redshift Ly \alpha surface brightness . The quasar-Ly \alpha emission cross-correlation we detect has a shape consistent with a linear \Lambda CDM model with \Omega _ { m } = 0.30 ^ { +0.10 } _ { -0.07 } . The predicted amplitude of this cross-correlation is proportional to the product of the mean Ly \alpha surface brightness , \langle \mu _ { \alpha } \rangle , the amplitude of mass density fluctuations , and the quasar and Ly \alpha emission bias factors . Using published cosmological observations to constrain the amplitude of mass fluctuations and the quasar bias factor , we infer the value of the product \langle \mu _ { \alpha } \rangle ( b _ { \alpha } / 3 ) = ( 3.9 \pm 0.9 ) \times 10 ^ { -21 } { erg } { s } ^ { -1 } cm ^ { -2 } Å ^ { -1 } arcsec ^ { -2 } , where b _ { \alpha } is the Ly \alpha emission linear bias factor . If the dominant sources of Ly \alpha emission we measure are star forming galaxies , we infer a total mean star formation rate density of { \rho } _ { SFR } = ( 0.28 \pm 0.07 ) ( 3 / b _ { \alpha } ) yr ^ { -1 } Mpc ^ { -3 } at z = 2 - 3.5 . For b _ { \alpha } = 3 , this value is a factor of 21 - 35 above previous estimates relying on individually detected Ly \alpha emitters , although it is consistent with the total star-formation density derived from dust-corrected , continuum UV surveys . Our observations therefore imply that 97 \% of the Ly \alpha emission in the Universe at these redshifts is undetected in previous surveys of Ly \alpha emitters . Our detected Ly \alpha emission is also much greater , by at least an order of magnitude , than that measured from stacking analyses of faint halos surrounding previously detected Ly \alpha emitters , but we speculate that it arises from similar low surface brightness Ly \alpha halos surrounding all luminous star-forming galaxies . We also detect a redshift space anisotropy of the quasar-Ly \alpha emission cross-correlation , finding evidence at the 3.0 \sigma level that it is radially elongated , contrary to the prediction for linear gravitational evolution , but consistent with distortions caused by radiative-transfer effects , as predicted by Zheng et al . ( 2011 ) . Our measurements represent the first application of the intensity mapping technique to optical observations .