The material and spectroscopic properties of Cr-doped Ca5(PO4)3F (FAP) were investigated using several different chemical and physical means. From analytical titration measurements the chromium in Cr:FAP was found to be tetravalent. ESR measurements detected a trace (0.5 - 10 ppm) of Cr5+ (3d1) and no evidence for Cr3+ (3d3). The absorption and emission spectra of Cr: FAP can be interpreted on the basis of Cr4+ (3d2) ions substituting for P within a distorted tetrahedron of oxygen ions. Calculated electronic (Stark) levels for Cr4+ based on an approximate site symmetry of C4 agree well with levels deduced from an analysis of the experimental optical data. The model Hamiltonian includes Coulombic parameters B and C, interconfiguration interaction terms and the spin-orbit coupling for the 3d2 atomic configuration of Cr4+ and crystal-field terms in C4 symmetry. The parametrized Hamiltonian was diagonalized within the complete d2 configuration. Both free ion and crystal field parameters are presented.