Radial velocity observations obtained at the Kitt Peak National Observatory in 1981, 1983, 1984, and 1991 confirm the suggestion made by McLaughlin six decades ago that the bright Algol-type binary δ Librae has a long-period companion. An analysis of this eclipsing system's barycentric velocity for these four epochs and four earlier ones where published observations were available yield these spectroscopic elements for its center of mass: P=2.762+/-0.001 yr, K=5.46+/-0.15 km s-1, e=0.28+/-0.05, ω=198deg+/-7deg, and T=1983.24+/-0.04. From these results, it can be inferred that the third star's mass and spectral type are 0.95+/-0.04 Msolar and G9 and that the entire δ Lib system is even more similar to the archetypal eclipsing binary β Persei (Algol) than was previously recognized. The spectroscopic orbital elements for the B9.5 V primary star in the eclipsing system are also updated.