  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.
