Radio Doppler data generated by the Deep Space Network (DSN) from five encounters of the Galileo spacecraft with Callisto, Jupiter's outermost Galilean satellite, have been used to determine the mass (GM) and unnormalized quadrupole gravity coefficients in Callisto's external gravitational field. The results are GM=(7179.292±0.009) km 3 s -2, J 2=(32.7±0.8)×10 -6, C 22=(10.2±0.3)×10 -6, S 22=(-1.1±0.3)×10 -6, C 21=(0.0±0.3)×10 -6, and S 21=(0.0±1.6)×10 -6. Also, four spacecraft images of Callisto have been used to determine its mean radius. The result is R=(2410.3±1.5) km, with no detectable deviation from sphericity. Derived parameters are Callisto's mean density of (1834.4±3.4) kg m -3 and axial moment of inertia C/MR 2=0.3549±0.0042. While the mean density indicates that Callisto is a mixture of rock and ice, the moment of inertia is too small for a homogeneous mixture. Accordingly, we present a suite of possible two- and three-layer interior models that satisfy the given constraints for radius, density, and moment of inertia. While not unique, these models show that Callisto cannot be entirely differentiated, and that there must exist a region of mixed ice and rock-metal, possibly extending to the center of the satellite.