We detect the large-scale structure of Lyα emission in the Universe at redshifts z = 2 − 3.5 by measuring the cross-correlation of Lyα 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 Lyα surface brightness. The quasar-Lyα emission cross-correlation we detect has a shape consistent with a linear ΛCDM model with Ω m = 0.30 +0.10 −0.07 . The predicted amplitude of this crosscorrelation is proportional to the product of the mean Lyα surface brightness, µ α , the amplitude of mass density fluctuations, and the quasar and Lyα 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 µ α (b α /3) = (3.9±0.9)×10 −21 erg s −1 cm −2Å−1 arcsec −2 , where b α is the Lyα emission linear bias factor. If the dominant sources of Lyα emission we measure are star forming galaxies, we infer a total mean star formation rate density of ρ SFR = (0.28 ± 0.07)(3/b α ) yr −1 Mpc −3 at z = 2 − 3.5. For b α = 3, this value is a factor of 21 − 35 above previous estimates relying on individually detected Lyα 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 Lyα emission in the Universe at these redshifts is undetected in previous surveys of Lyα emitters. Our detected Lyα emission is also much greater, by at least an order of magnitude, than that measured from stacking analyses of faint halos surrounding previously detected Lyα emitters, but we speculate that it arises from similar low surface brightness Lyα halos surrounding all luminous star-forming galaxies. We also detect a redshift space anisotropy of the quasar-Lyα emission cross-correlation, finding evidence at the 3.0σ 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.