  Based on a realistic spin Hamiltonian for a frustrated quasi-two dimensional
spin-1/2 antiferromagnet Cs$_{2}$CuCl$_{4}$, a three-dimensional spin ordering
in the applied magnetic field $B$ near the saturation value $B_{c}$ is studied
within the magnon Bose-Einstein condensation (BEC) scenario. With the use of a
hard-core boson formulation of the spin model, a strongly anysotropic magnon
dispersion in Cs$_{2}$CuCl$_{4}$ is calculated. In the dilute magnon limit near
$B_{c}$, the hard-core boson constraint is resulted in an effective magnon
interaction which is treated in the Hartree-Fock approximation. The critical
temperature $T_{c}$ is calculated as a function of a magnetic field $B$ and
compared with the phase boundary $T_{c}(B) $ experimentally determined in
Cs$_{2}$CuCl$_{4}$ [Phys. Rev. Lett. \textbf{95}, 127202 (2005)].
