We report, to the best of our knowledge, the first super-octave femtosecond polycrystalline Cr:ZnS laser at the central wavelength 2.4 µm. The laser is based on a non-polarizing astigmatic X-folded resonator with normal incidence mounting of the gain element. The chromatic dispersion of the resonator is controlled with a set of dispersive mirrors within one third of an optical octave over 2.05–2.6 µm range. The resonator’s optics is highly reflective in the range 1.8–2.9 µm. The components of the oscillator’s output spectrum at the wavelengths 1.6 µm and 3.2 µm are detected at –60 dB with respect to the main peak. Average power of few-cycle Kerr-lens mode-locked laser is 1.4 W at the pulse repetition frequency 79 MHz. That corresponds to 22% conversion of cw radiation of Er-doped fiber laser, which we used for optical pumping of the Cr:ZnS oscillator.