A comprehensive investigation of the frequency-noise spectral density of a free-running midinfrared quantum-cascade laser is presented for the first time. It provides direct evidence of the leveling of this noise down to a white-noise plateau, corresponding to an intrinsic linewidth of a few hundred hertz. The experiment is in agreement with the most recent theory on the fundamental mechanism of line broadening in quantum-cascade lasers, which provides a new insight into the Schawlow-Townes formula and predicts a narrowing beyond the limit set by the radiative lifetime of the upper level.