(Abridged) We detect the large-scale structure of Lya emission in the Universe at redshifts z=2-3.5 by measuring the cross-correlation of Lya surface brightness with quasars in SDSS/BOSS. We use a million spectra targeting Luminous Red Galaxies at z<0.8, after subtracting a best fit model galaxy spectrum from each one, as an estimate of the high-redshift Lya surface brightness. The quasar-Lya emission cross-correlation we detect has a shape consistent with a LambdaCDM 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 Lya surface brightness, <mu_alpha>, the amplitude of mass fluctuations, and the quasar and Lya emission bias factors. Using known values, we infer <mu_alpha>(b_alpha/3) = (3.9 +/- 0.9) x 10^-21 erg/s cm^-2 A^-1 arcsec^-2, where b_alpha is the Lya emission bias factor. If the dominant sources of Lya emission are star forming galaxies, we infer rho_SFR = (0.28 +/- 0.07) (3/b_alpha) /yr/Mpc^3 at z=2-3.5. For b_alpha=3, this value is a factor of 21-35 above previous estimates from individually detected Lya emitters, although consistent with the total rho_SFR derived from dust-corrected, continuum UV surveys. 97% of the Lya emission in the Universe at these redshifts is therefore undetected in previous surveys of Lya emitters. Our measurement is much greater than seen from stacking analyses of faint halos surrounding previously detected Lya emitters, but we speculate that it arises from similar Lya halos surrounding all luminous star-forming galaxies. We also detect redshift space anisotropy of the quasar-Lya emission cross-correlation, finding evidence at the 3.0 sigma level that it is radially elongated, consistent with distortions caused by radiative-transfer effects (Zheng et al. (2011)). Our measurements represent the first application of the intensity mapping technique to optical observations.
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