The compound GaP1−xNx is highly attractive to pseudomorphically integrate red-light emitting devices and photovoltaic cells with the standard Si technology because it is lattice matched to Si with a direct bandgap energy of ≈1.96 eV for x = 0.021. Here, we report on the chemical beam epitaxy of GaP1−xNx alloys on nominally (001)-oriented GaP-on-Si substrates. The incorporation of N into GaP1−xNx was systematically investigated as a function of growth temperature and the fluxes of the N and P precursors, 1,1-dimethylhydrazine (DMHy) and tertiarybutylphosphine (TBP), respectively. We found that the N mole fraction exhibits an Arrhenius behavior characterized by an activation energy of (0.79 ± 0.05) eV. With respect to the fluxes, we determined that the N mole fraction is linearly proportional to the flux of DMHy and inversely proportional to the one of TBP. All results are summarized in a universal equation that describes the dependence of x on the growth temperature and the fluxes of the group-V precursors. The results are further illustrated in a growth diagram that visualizes the variation of x as the growth temperature and the flux of DMHy are varied. This diagram also shows how to obtain single-phase and flat GaP1−xNx layers, as certain growth conditions result in chemically phase-separated layers with rough surface morphologies. Finally, our results demonstrate the feasibility of chemical beam epitaxy to obtain single-phase and flat GaP1−xNx layers with x up to about 0.04, a value well above the one required for the lattice-matched integration of GaP1−xNx-based devices on Si.