The absolute scale of the neutrino mass plays a critical role in physics at every scale, from the subatomic to the cosmological. Measurements of the tritium end-point spectrum have provided the most precise direct limit on the neutrino mass scale. In this Letter, we present advances by Project 8 to the cyclotron radiation emission spectroscopy (CRES) technique culminating in the first frequency-based neutrino mass limit. With only a cm^{3}-scale physical detection volume, a limit of m_{β}<155 eV/c^{2} (152 eV/c^{2}) is extracted from the background-free measurement of the continuous tritium beta spectrum in a Bayesian (frequentist) analysis. Using ^{83m}Kr calibration data, a resolution of 1.66±0.19 eV (FWHM) is measured, the detector response model is validated, and the efficiency is characterized over the multi-keV tritium analysis window. These measurements establish the potential of CRES for a high-sensitivity next-generation direct neutrino mass experiment featuring low background and high resolution.