The superconducting gap structure of recently discovered heavy fermion CePt_3Si without spatial inversion symmetry was investigated by thermal transport measurements down to 40 mK. In zero field a residual T-linear term was clearly resolved as T-> 0, with a magnitude in good agreement with the value expected for a residual normal fluid with a nodal gap structure, together with a T^2-dependence at high temperatures. With an applied magnetic fields, the thermal conductivity grows rapidly, in dramatic contrast to fully gapped superconductors, and exhibits one-parameter scaling with T/sqrt{H}. These results place an important constraint on the order parameter symmetry, that is CePt_3Si is most likely to have line nodes.
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