  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.
