  We report ^{11}B and ^{195}Pt NMR measurements in non-centrosymmetric
superconductor Li_2Pt_3B. We find that the spin susceptibility measured by the
Knight shift remains unchanged across the superconducting transition
temperature T_c. With decreasing temperature (T) below T_c, the spin-lattice
relaxation rate 1/T_1 decreases with no coherence peak and is in proportion to
T^3. These results indicate that the Cooper pair is in the spin-triplet state
and that there exist line nodes in the superconducting gap function. They are
in sharp contrast with those in the isostructural Li_2Pd_3B which is a
spin-singlet, s-wave superconductor, and are ascribed to the enhanced
spin-orbit coupling due to the lack of spatial inversion symmetry. Our finding
points to a new paradigm where exotic superconductivity arises in the absence
of strong electron-electron correlations.
