A Compton polarimeter has been installed in Hall A at Jefferson Laboratory. This letter reports on the first electron beam polarization measurements performed during the HAPPEX experiment at an electron energy of 3.3 GeV and an average current of 40 $\mu$A. The heart of this device is a Fabry-Perot cavity which increased the luminosity for Compton scattering in the interaction region so much that a 1.4% statistical accuracy could be obtained within one hour, with a 3.3% total error.
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