Compton backscattering polarimetry provides a fast and accurate method to measure the polarization of an electron beam in a storage ring. Since the method is non-destructive, the polarization of the electron beam can be monitored during internal target experiments. For this reason, a Compton polarimeter has been constructed at NIKHEF to measure the polarization of the longitudinally polarized electrons which can be stored in the AmPS ring. The design and results of the polarimeter, the first Compton polarimeter to measure the polarization of a stored longitudinally polarized electron beam directly, are presented in this paper.