We present a first implementation of optical-frequency-comb-based rapid trace gas detection in the molecular fingerprint region in the mid-infrared. Near-real-time acquisition of broadband absorption spectra with 0.0056 cm(-1) maximum resolution is demonstrated using a frequency comb Fourier transform spectrometer which operates in the 2100-to-3700-cm(-1) spectral region. We achieve part-per-billion detection limits in 30 seconds of integration time for several important molecules including methane, ethane, isoprene, and nitrous oxide. Our system enables precise concentration measurements even in gas mixtures that exhibit continuous absorption bands, and it allows detection of molecules at levels below the noise floor via simultaneous analysis of multiple spectral features.