Frequency combs with a wide instantaneous spectral span covering the 3–20 µm molecular fingerprint region are highly desirable for broadband and high-resolution frequency comb spectroscopy, trace molecular detection, and remote sensing. We demonstrate a novel approach for generating high-average-power middle-infrared (MIR) output suitable for producing frequency combs with an instantaneous spectral coverage close to 1.5 octaves. Our method is based on utilizing a highly-efficient and compact Kerr-lens mode-locked Cr2+:ZnS laser operating at 2.35-µm central wavelength with 6-W average power, 77-fs pulse duration, and high 0.9-GHz repetition rate; to pump a degenerate (subharmonic) optical parametric oscillator (OPO) based on a quasi-phase-matched GaAs crystal. Such subharmonic OPO is a nearly ideal frequency converter capable of extending the benefits of frequency combs based on well-established mode-locked pump lasers to the MIR region through rigorous, phase- and frequency-locked down conversion. We report a 0.5-W output in the form of an ultra-broadband spectrum spanning 3–8 µm measured at 50-dB level.