  The absolute scale of the neutrino mass plays a critical role in physics at
every scale, from the particle to the cosmological. Measurements of the tritium
endpoint 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_\beta{<}$155 eV ($152$ eV) is extracted from
the background-free measurement of the continuous tritium beta spectrum in a
Bayesian (frequentist) analysis. Using $^{83{\rm m}}$Kr calibration data, an
improved resolution of 1.66${\pm}$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.
