The two most recent and precise measurements of the charged kaon mass use X-rays from kaonic atoms and report uncertainties of 14 ppm and 22 ppm yet differ from each other by 122 ppm. We describe the possibility of an independent mass measurement using the measurement of Cherenkov light from a narrow-band beam of kaons, pions, and protons. This technique was demonstrated using data taken opportunistically by the Main Injector Particle Production experiment at Fermi National Accelerator Laboratory which recorded beams of protons, kaons, and pions ranging in momentum from +37 GeV/c to +63 GeV/c. The measured value is 491.3 +/- 1.7 MeV/c^2, which is within 1.4 sigma of the world average. An improvement of two orders of magnitude in precision would make this technique useful for resolving the ambiguity in the X-ray data and may be achievable in a dedicated experiment.
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