We studied the evolution of superconductivity (sc) and antiferromagnetism (afm) in the heavy fermion compound CePt3Si with hydrostatic pressure. We present a pressure-temperature phase diagram established by electrical transport measurements. Pressure shifts the superconducting transition temperature, Tc, to lower temperatures. Antiferromagnetism is suppressed at a critical pressure Pc ≈ 0.5 GPa.Key words: CePt3Si, superconductivity, antiferromagnetism, hydrostatic pressure Superconductivity (sc) is one of the most striking effects in solid state physics. In a conventional superconductor Cooper pairing is mediated by phonons. In general, magnetism destroys superconductivity. In heavy fermion systems, however, sc exists in close proximity to magnetism, promoting the suspicion that the sc is mediated by magnetic excitations. Since the discovery of sc in the heavy fermion compound CeCu2Si2 at atmospheric pressure [1], only a few Ce-based systems were found which also exhibit sc at atmospheric pressure, like CeMIn5 (M=Co, Ir) [4]. Most superconducting pure Ce-based systems show sc only under applied pressure sufficient to suppress long range magnetic order, like CeIn3 [2] or CeRh2Si2 [3]. CeIn3 displays a typical temperature-pressure phase diagram for these compounds; antiferromagnetism (afm) is suppressed to zero temperature with pressure and sc develops right in the vicinity where afm disappears [2]. Very recently another material, namely CePt3Si, was found showing magnetic order and sc at atmospheric pressure [5]. In contrast to the systems mentioned before, the crystal * Corresponding Author: Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Str. 40, 01187 Dresden, Germany. Phone: +49 (0)351 4646 3127, Fax: +49 (0)351 4646 3119, Email: nicklas@cpfs.mpg.de structure of CePt3Si is non-centrosymmetric, which is believed to allow for novel superconducting order parameter states. In this work we investigate the pressure dependence of the superconducting transition temperature, Tc, and of the Néel temperature, TN , by electrical resistivity, ρ, measurements to study the interplay of magnetism and sc in CePt3Si.Polycrystalline CePt3Si was prepared by high frequency melting, followed by a heat treatment at 870 • C for 10 days. The phase purity was checked by x-ray diffraction and electron microprobe measurements. CePt3Si crystallizes in a tetragonal structure with no center of inversion symmetry. At ambient pressure CePt3Si orders antiferromagnetically at TN = 2.2 K and sc develops out of the antiferromagnetic state bellow Tc = 0.75 K [5]. At higher temperatures, the resistivity shows two pronounced curvatures at 75 K and 15 K [5]. These features seem to be related to crystal electric field effects in the presence of Kondo-type interactions.The sample was mounted in a clamp-type pressure cell with a 1:1 mixture of n-pentane and 2-methylbutane as pressure medium. The measured pressure shift of the superconducting transition temperature of tin served as pressure gauge. A standard 4-point LockIn techn...