We measure the large-scale cross-correlation of quasars with the Lyα forest absorption in redshift space, using ∼ 60000 quasar spectra from Data Release 9 (DR9) of the Baryon Oscillation Spectroscopic Survey (BOSS). The cross-correlation is detected over a wide range of scales, up to comoving separations r of 80 h-1Mpc. For r > 15 h-1Mpc, we show that the cross-correlation is well fitted by the linear theory prediction for the mean overdensity around a quasar host halo in the standard ΛCDM model, with the redshift distortions indicative of gravitational evolution detected at high confidence. Using previous determinations of the Lyα forest bias factor obtained from the Lyα autocorrelation, we infer the quasar bias factor to be bq = 3.64+0.13-0.15 at a mean redshift z = 2.38, in agreement with previous measurements from the quasar auto-correlation. We also obtain a new estimate of the Lyα forest redshift distortion factor, βF = 1.1±0.15, slightly larger than but consistent with the previous measurement from the Lyα forest autocorrelation. The simple linear model we use fails at separations r < 15h-1Mpc, and we show that this may reasonably be due to the enhanced ionization due to radiation from the quasars. We also provide the expected correction that the mass overdensity around the quasar implies for measurements of the ionizing radiation background from the line-of-sight proximity effect.© 2013 IOP Publishing Ltd and Sissa Medialab srl.