Selenographic coordinates for about 6000 lunar points identified on the Lunar Orbiter photographs are tabulated and have been combined with those lunar radii derived from the Apollo 15 laser altimeter data. These coordinates were used to derive that triaxial ellipsoid which best fits the Moon's irregular surface. Fits where obtained for different constraints on both the axial orientations and the displacement of the center of the ellipsoid. The semiaxes for the unconstrained ellipsoid were a = 1737.6 km, b = 1735.6 km, and c = 1735.0 km which correspond to a mean radius of about 1736.1 km. These axes were found to be nearly parallel to the Moon's principal axes of inertia, and the origin was displaced about 2.0 km from the Moon's center of gravity in a direction away from the Earth and to the south of the lunar equator.