We report on the highest precision yet achieved in the measurement of the polarization of a lowenergy, O(1 GeV), continuous wave (CW) 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 microstrip 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 µA, 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 Q weak experiment, a measurement of the weak vector 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 the first use of diamond detectors for particle tracking in an experiment. It demonstrates the stable operation of a diamond based tracking detector in a high radiation environment, for two years.