  We studied the evolution of superconductivity (sc) and antiferromagnetism
(afm) in the heavy fermion compound CePt_3Si with hydrostatic pressure. We
present a pressure-temperature phase diagram established by electrical
transport measurements. Pressure shifts the superconducting transition
temperature, T_c, to lower temperatures. Antiferromagnetism is suppressed at a
critical pressure P_c=0.5 GPa.
