  We present the first measurement of the large-scale cross-correlation of
Lyman alpha forest absorption and Damped Lyman alpha systems (DLA), using the
9th Data Release of the Baryon Oscillation Spectroscopic Survey (BOSS). The
cross-correlation is clearly detected on scales up to 40 Mpc/h and is well
fitted by the linear theory prediction of the standard Cold Dark Matter model
of structure formation with the expected redshift distortions, confirming its
origin in the gravitational evolution of structure. The amplitude of the
DLA-Lyman alpha cross-correlation depends on only one free parameter, the bias
factor of the DLA systems, once the Lyman alpha forest bias factors are known
from independent Lyman alpha forest correlation measurements. We measure the
DLA bias factor to be b_D = (2.17 +/- 0.20) beta_F^{0.22}, where the Lyman
alpha forest redshift distortion parameter beta_F is expected to be above
unity. This bias factor implies a typical host halo mass for DLAs that is much
larger than expected in present DLA models, and is reproduced if the DLA cross
section scales with halo mass as M_h^alpha, with alpha= 1.1 +/- 0.1 for
beta_F=1. Matching the observed DLA bias factor and rate of incidence requires
that atomic gas remains extended in massive halos over larger areas than
predicted in present simulations of galaxy formation, with typical DLA proper
sizes larger than 20 kpc in host halos of masses ~ 10^12 solar masses. We infer
that typical galaxies at z ~ 2 to 3 are surrounded by systems of atomic clouds
that are much more extended than the luminous parts of galaxies and contain ~
10% of the baryons in the host halo.
