The CH radical offers a sensitive way to test the hypothesis that fundamental constants measured on earth may differ from those observed in other parts of the universe. The starting point for such a comparison is to have accurate laboratory frequencies. Here, we measure the frequency of the lowest millimeter-wave transition of CH, near 535 GHz, with an accuracy of 0.6 kHz. This improves the uncertainty by roughly two orders of magnitude over previous determinations and opens the way for sensitive new tests of varying constants.