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The Compton scattering of a circularly polarized photon beam and a polarized electron beam leads to an asymmetric spatial distribution of the gamma rays. This asymmetry has been calculated for the high intensity gamma-ray source (HIGS) beam at Duke University. Owing to the high intensity of the HIGS beam, this asymmetry is determined to be measurable with a small statistical error using a simple optical imaging system for gamma-ray beams. We propose to set up this system to measure the polarization of the electron beam in the Duke storage ring.