We introduce a novel formulation of the Circle Hough Transform that we call the Coherent Circle Hough Transform. The technique uses phase to code for radii of circles. The usual simplifications of the Circle Hough Transform (CHT) are used in which lines pointing away from edge points are plotted rather than circles. Intersections of these "spokes" accumulate edge magnitude, or edge "energy", near the centres of circles. We introduce the use of a complex accumulator space and allow each spoke to vary in phase along its length. The spokes are in phase near the centre of circles and out of phase elsewhere. The spokes generated by noise are in random phase and destructively interfere. We present results for an isolated circle with additive white Gaussian noise for both the conventional Energy CHT and the new Coherent CHT. The results demonstrate that the technique reduces the mean and variance of the background level in the accumulator array, that the peak to background level improves, and that the peak width is reduced improving localisation of circle centres.