The hyperfine interaction between a Pu3+ ion in CaF2 and the surrounding fluorine ligand nuclei has been measured by the electron-nuclear double-resonance (ENDOR) method. The interaction can be expressed in terms of a Hamiltonian AsS-->'.I-->+Ap(3S'zIz- S-->'.I-->), where z is along the bond axis. The parameters found for the nearest-neighbor fluorine nuclei are As=-13.39+/-0.01 MHz and Ap=-0.135+/-0.01 MHz. The absolute signs of As and Ap were determined by a double ENDOR experiment. The results show that effects due to covalency are much more pronounced in this actinide ion than in ions of the lanthanide series. Measurements of the plutonium (or self-) ENDOR are also reported and the ground-state crystalline-field splitting is shown to be 348 +/- 25 cm-1.