We report on the highest precision yet achieved in the measurement of the polarization of a low energy, $mathcal{O}$(1 GeV), electron beam, accomplished using a new polarimeter based on electron-photon scattering, in Hall~C at Jefferson Lab. A number of technical innovations were necessary, including a novel method for precise control of the laser polarization in a cavity and a novel diamond micro-strip detector which was able to capture most of the spectrum of scattered electrons. The data analysis technique exploited track finding, the high granularity of the detector and its large acceptance. The polarization of the $180~mu$A, $1.16$~GeV electron beam was measured with a statistical precision of $<$~1% per hour and a systematic uncertainty of 0.59%. This exceeds the level of precision required by the qweak experiment, a measurement of the vector weak charge of the proton. Proposed future low-energy experiments require polarization uncertainty $<$~0.4%, and this result represents an important demonstration of that possibility. This measurement is also the first use of diamond detectors for particle tracking in an experiment.
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