  We investigate the extended Heisenberg model on the Kagome lattice by using
Gutzwiller projected fermionic states and the variational Monte Carlo
technique. In particular, when both second- and third-neighbor super-exchanges
are considered, we find that a gapped spin liquid described by non-trivial
magnetic fluxes and long-range chiral-chiral correlations is energetically
favored compared to the gapless U(1) Dirac state. Furthermore, the topological
Chern number, obtained by integrating the Berry curvature, and the degeneracy
of the ground state, by constructing linearly independent states, lead us to
identify this flux state as the chiral spin liquid with $C=1/2$ fractionalized
Chern number.
