  We construct the hydrodynamic theory of coherent collective motion
("flocking") at a solid-liquid interface. The polar order parameter and
concentration of a collection of "active" (self-propelled) particles at a
planar interface between a passive, isotropic bulk fluid and a solid surface
are dynamically coupled to the bulk fluid. We find that such systems are
stable, and have long-range orientational order, over a wide range of
parameters. When stable, these systems exhibit "giant number fluctuations",
i.e., large fluctuations of the number of active particles in a fixed large
area. Specifically, these number fluctuations grow as the $3/4$th power of the
mean number within the area. Stable systems also exhibit anomalously rapid
diffusion of tagged particles suspended in the passive fluid along any
directions in a plane parallel to the solid-liquid interface, whereas the
diffusivity along the direction perpendicular to the plane is non-anomalous. In
other parameter regimes, the system becomes unstable.
