We present a sequence of three Doppler images of the spotted RS CVn star UX Arietis obtained over a 5-month interval from August 1986 through January 1987. The spot distribution was quite complex and consisted of a large stable polar spot, a spot near the equator, and several other spots at intermediate positive and negative latitudes. The time intervals between successive images were small enough that we were able to reliably track the evolution of the spot distribution, measuring accurate longitudes, latitudes, and areas of the major spots, as well as their drift rates in longitude and latitude. The longitudinal drifts of spot features at equatorial, intermediate, and high latitudes yielded an accurate measurement of differential rotation. We find that the spotted primary of UX Arietis is indeed rotating differentially and in the sense opposite to that of the Sun, i.e. the poles rotate faster than the equator. The equator is synchronized to the orbital angular velocity, and the angular velocity increases towards either pole. The angular velocity distribution can be expressed as Ω(°/day) = −55.91 + 1.09(±0.09) sin2∅, where ∅ is the latitude. The amount of differential rotation, parameterized as the ratio of the difference between the equatorial and polar angular velocities to the equatorial angular velocity, is then α = −0.020(±0.002), as compared to a value of α = +0.2 for the Sun.