We consider the role of magnetic fields on the broken inversion superconductor CePt3Si. We show that upper critical field for a field along the c-axis exhibits a much weaker paramagnetic effect than for a field applied perpendicular to the c-axis. The in-plane paramagnetic effect is strongly reduced by the appearance of helical structure in the order parameter. We find that to get good agreement between theory and recent experimental measurements of Hc2, this helical structure is required. We propose a Josephson junction experiment that can be used to detect this helical order. In particular, we predict that Josephson current will exhibit a magnetic interference pattern for a magnetic field applied perpendicular to the junction normal. We also discuss unusual magnetic effects associated with the helical order. PACS numbers: The recently discovered heavy fermion superconductor CePt 3 Si 1 has triggered many experimental and theoretical studies 2,3,4,5,6,7,8,9. There are two features which have caused this attention: the absence of inversion symmetry; and the comparatively high upper critical magnetic field (H c2). Broken inversion symmetry (parity) has a pronounced effect on the quasiparticle states through the splitting of the two spin degenerate bands. This influences the superconducting phase, which usually relies on the formation of pairs of electrons in degenerate quasi-particle states with opposite momentum. The availability of such quasiparticle states is usually guaranteed by time reversal and inversion symmetries (parity) 10,11. It is relatively easy to remove time reversal symmetry, e.g. by a magnetic field, and the physical consequences of this have been well studied. However, parity is not so straightforwardly manipulated by external fields. Super-conductivity in materials without inversion center therefore provides a unique opportunity in this respect. The large H c2 ≈ 4T in CePt 3 Si 1,8 implies that the Zee-man splitting must be non-negligible below T c = 0.75K (the estimated paramagnetic limit is at H P ≈ 1.2 T). In a magnetic field, this superconductor has to form Cooper pairs under rather odd circumstances. In particular, it is no longer guaranteed that a state with momentum k at the Fermi surface has a degenerate partner at −k. The state k would rather pair with a degenerate state −k + q and in this way generate an inhomogeneous su-perconducting phase. We argue below that recent H c2 measurements 8 suggest that this is the case in CePt 3 Si. These measurements show that, while the upper critical field is basically isotropic close to T c , a small anisotropy appears at lower temperature 8 (H c c2 /H ab c2 = 1.18 at T = 0). The apparent absence of a paramagnetic limit in CePt 3 Si can be explained by lack of inversion symmetry even if the pairing has s-wave symmetry 2,12,13. However, these works indicate that suppression of paramagnetism is very anisotropic and the application of this theory to CePt 3 Si would indicate no paramagnetic suppression for the field along the c-axis, but a suppression ...