It has long been proposed that doping a chiral spin liquid (CSL) or fractional quantum Hall state can give rise to topological superconductivity. Despite of intensive effort, definitive evidences still remain lacking. We address this problem by studying the $t$-$J$ model supplemented by time-reversal symmetry breaking chiral interaction $J_chi$ on the triangular lattice using density-matrix renormalization group with a finite concentration $delta$ of doped holes. It has been established that the undoped, i.e., $delta$=0, system has a CSL ground state in the parameter region $0.32le J_chi/J le 0.56$. Upon light doping, we find that the ground state of the system is consistent with a Luther-Emery liquid with power-law superconducting and charge-density-wave correlations but short-range spin-spin correlations. In particular, the superconducting correlations, whose pairing symmetry is consistent with $dpm id$-wave, are dominant at all hole doping concentrations. Our results provide direct evidences that doping the CSL on the triangular lattice can naturally give rise to topological superconductivity.
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