We report observation of hyperfine quantum beats in the light emitted by the $7{^{2}P}_{\frac{3}{2}}$ level of ${\mathrm{Cs}}^{133}$ after excitation by a short resonant dye laser pulse. Frequency analysis of the beats provides a measurement of the hyperfine splittings in agreement with previous work. The usefulness of quantum-beat detection as a new method of laser spectroscopy without complications from the Doppler effect is discussed.