The lens system 0957+561 is the first gravitational lens system to be discovered and the first for which a time delay was measured. Because the system is unusually rich in observables such as image positions, fluxes, VLBI structure, and polarization it has been modeled quite extensively. However, since it resides in a cluster providing substantial convergence, the velocity dispersion of the lensing galaxy is an important component to models. We have measured this dispersion to be 288 ± 9 km s⁻¹ (1 σ), which implies a Hubble constant of 72±7 km s⁻¹ Mpc⁻¹ (1 σ) according to the preferred fine guidance sensors model of Grogin and Narayan and 70±7 km s⁻¹ Mpc⁻¹ (1 σ) using the softened power-law sphere model. The unknown velocity dispersion anisotropy of the central galaxy produces an additional uncertainty of perhaps 15% or more. We see no variation in dispersion with position to a radius of ± 3''. In addition to a galaxy from the background cluster at z=0.5, our slit serendipitously picked up a galaxy at z=0.448 and two galaxies that may be part of a background cluster at a redshift of z=0.91.