The Gravity Probe B (GP-B) satellite experiment will measure the precession of on-board gyroscopes to extraordinary accuracy. Such precessions are predicted by General Relativity (GR), and one component of this precession is the "frame-dragging" or Lense-Thirring effect, which is caused by the rotation of the Earth. A new theory of gravity, which passes the same extant tests of GR, predicts, however, a second and much larger "frame-dragging" precession. The magnitude and signature of this larger effect is given for comparison with the GP-B data.