We present a new technique suitable for generating broadband phase- and frequency-locked frequency combs in the mid-infrared. Our source is based on a degenerate optical parametric oscillator (OPO) which rigorously both down-converts and augments the spectrum of a pump frequency comb provided by a commercial mode-locked near-IR laser. Low intracavity dispersion, combined with extensive cross-mixing of comb components, results in extremely broad instantaneous mid-IR bandwidths. We achieve an output power of 60 mW and 20 dB bandwidth extending from 2500 to 3800 nm. Among other applications, such a source is well-suited for coherent Fourier-transform spectroscopy in the absorption-rich mid-IR 'molecular fingerprint' region.