Generic violations of Lorentz symmetry can be described by an effective field theory framework that contains both general relativity and the Standard Model of particle physics called the Standard-Model extension (SME). We obtain new constraints on the gravitational sector of the SME using recently published final results from Gravity Probe B. These include for the first time an upper limit at the 10_3 level on the time-time component of the new tensor field responsible for inducing local Lorentz violation in the theory, and an independent limit at the 10_7 level on a combination of components of this tensor field.