We present measurements of the ratio of the proton elastic electromagnetic form factors, μpGEp/GMp. The Jefferson Lab Hall A Focal Plane Polarimeter was used to determine the longitudinal and transverse components of the recoil proton polarization in ep elastic scattering; the ratio of these polarization components is proportional to the ratio of the two form factors. These data reproduce the observation of Jones et al. [Phys. Rev. Lett. 84, 1398 (2000)], that the form factor ratio decreases significantly from unity above Q2=1 GeV2.