High-precision measurements of the proton elastic form-factor ratio, mu pG p E/G p M, have been made at four-momentum transfer, Q2, values between 0.2 and 0.5 GeV2. The new data, while consistent with previous results, clearly show a ratio less than unity and significant differences from the central values of several recent phenomenological fits. By combining the new form-factor ratio data with an existing cross-section measurement, one finds that in this Q2 range the deviation from unity is primarily due to G p E being smaller than expected.