An ab initio molecular orbital study has been carried out for the C3P radical and its positive ion, C3P+. Geometries, vibrational frequencies, and infrared intensities have been obtained at the MP2/6-31G* level, whereas MP4 theory has been employed to compute electronic energies. A topological analysis of the electron density for nonlinear species has also been carried out. The neutral species is predicted to have a linear ground state (2 Pi electronic state), the next lowest-lying isomer (about 15 kcal/mol higher in energy) being a rhomboidal species with B-2(1) electronic state. Both isomers have high dipole moments, 2.773 and 3.893 D, respectively, which should favor their experimental detection. In the case of the cation the ground state is also predicted to be a linear structure ((3) Sigma(-) electronic state). The next low-lying isomer is a triplet rhomboidal structure which lies about 10 kcal/mol higher than the C3P+ ground state at correlated levels. Therefore, it seems that, Like their sulfur analogues and contrary to the silicon compounds, the CnP species have linear ground states.