  We consider the phase diagram of a spatially anisotropic 2D triangular
antiferromagnet in a magnetic field. Classically, the ground state is
umbrella-like for all fields, but we show that the quantum phase diagram is
much richer and contains a 1/3 magnetization plateau, two commensurate planar
states, two incommensurate chiral umbrella phases, and, possibly, a planar
state separating the two chiral phases. Our analysis sheds light on several
recent experimental findings for the spin-1/2 system Cs_2CuBr_4.
