© 2016 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. We present a tentative detection of the large-scale structure of Ly α emission in the Universe at redshifts z = 2-3.5 by measuring the cross-correlation of Ly α surface brightness with quasars in Sloan Digital Sky Survey/Baryon Oscillation Spectroscopic Survey.We use amillion spectra targeting luminous red galaxies at z < 0.8, after subtracting a best-fitting model galaxy spectrum from each one, as an estimate of the high-redshift Ly α surface brightness. The quasar- Ly α emission cross-correlation is detected on scales 1 ~ 15 h-1Mpc, with shape consistent with a Λ (CDM model with) Ωm= 0.30+0.10-0.07. The predicted amplitude of this cross-correlation is proportional to the product of the mean Ly α surface brightness, (μα), the amplitude of mass fluctuations and the quasar and Lyαemission bias factors. We infer (μα) (bα/3) = (3.9 ± 0.9) × 10-21 erg s-1 cm-2 Å-1 arcsec-2, where bαis the Ly α emission bias. If star-forming galaxies dominate this emission, we find ρSFR = (0.28 ± 0.07)(3/bα) yr-1Mpc-3. For bα= 3, this value is~30 times larger than previous estimates from individually detected Ly α emitters, but consistent with the total ρSFR derived from dust-corrected, continuum UV galaxy surveys, if most of the Ly α photons from these galaxies avoid dust absorption and are reemitted after diffusing in large gas haloes. Heating of intergalactic gas by He II photoionization from quasar radiation or jets may alternatively explain the detected correlation, and cooling radiation from gas in galactic haloes may also contribute. We also detect redshift space anisotropy of the quasar-Ly α emission cross-correlation, finding evidence at the 3.0σ level that it is radially elongated, which may be explained by radiative-transfer effects. Our measurements represent the first application of the intensity mapping technique to optical observations.