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