  In this paper a semilinear elliptic PDE with rapidly oscillating coefficients
is homogenized. The novetly of our result lies in the fact that we allow the
second order part of the differential operator to be degenerate in some portion
of $\R^d$.\\ Our fully probabilistic method is based on the connection between
PDEs and BSDEs with random terminal time and the weak convergence of a class of
diffusion processes.
