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Pyrite FeS₂ is a potentially ideal absorber for thin film solar cells as it is composed of earth-abundant, inexpensive elements, has a suitable band gap (0.95 eV), and is strongly absorptive. Lack of doping control, however, has precluded p-n homojunctions. Heterojunction solar cells have disappointing efficiencies (≤3 %), likely limited by a leaky surface inversion layer. The ability to controllably n- and p-dope FeS₂ would make possible a homojunction solar cell that could, uniquely, avoid this surface inversion entirely. Recently, we established S vacancies as n-dopants in FeS₂ and achieved transport control in bulk crystals. Here, we demonstrate p-doping by introducing phosphorus (P) during growth. Increasing P concentrations above ~40 ppm triggers a majority carrier inversion from n- to p-type. Thermal activation energy, room temperature hole density, and mobility in p-type crystals are ~170 meV, ~10¹⁸ cm^-3, and 1 cm²V^-1s^-1, respectively. Density functional theory confirms that P substitution for S creates an acceptor level 100’s of meV from the valence band, in agreement with experiment. With p-type control thus achieved, p-n FeS₂ homojunctions now become possible.