The p-type semiconductor Cu3PSe4 has recently been established to have a direct bandgap of 1.4 eV and an optical absorption spectrum similar to GaAs [Applied Physics Letters, 99, 181903 (2011)], suggesting a possible application as a solar photovoltaic absorber. Here we calculate the thermodynamic stability, defect energies and concentrations, and several material properties of Cu3PSe4 using a wholly GGA+U method (the generalized gradient approximation of density functional theory with a Hubbard U term included for the Cu-d orbitals). We find that two low energy acceptor defects, the copper vacancy VCu and the phosphorus-on-selenium antisite PSe, establish the p-type behavior and likely prevent any n-type doping near thermal equilibrium. The GGA+U defect calculation method is shown to yield more accurate results than the more standard method of applying post-calculation GGA+U -based bandgap corrections to strictly GGA defect calculations.