  We report on results of specific heat measurements on single crystals of the
frustrated quasi-2D spin-1/2 antiferromagnet Cs_2CuCl_4 (T_N=0.595 K) in
external magnetic fields B<12 T and for temperatures T>30 mK. Decreasing B from
high fields leads to the closure of the field-induced gap in the magnon
spectrum at a critical field B_c = 8.51 T and a magnetic phase transition is
clearly seen below B_c. In the vicinity to B_c, the phase transition boundary
is well described by the power-law T_c(B)\propto (B_c-B)^{1/\phi} with the
measured critical exponent \phi\simeq 1.5. These findings are interpreted as a
Bose-Einstein condensation of magnons.
