We present a new, to the best of our knowledge, approach for self-heterodyne optical frequency comb (OFC) spectroscopy in which a single Mach-Zehnder modulator is utilized to generate both an optical frequency comb and a frequency-shifted local oscillator. This method allows for coherent, time-domain averaging to be performed without the need for feedback mechanisms or software corrections. As an initial demonstration, we have measured acetylene rovibrational transition frequencies with coherently averaged comb spectra. Spectra averaged for less than 10 s yielded standard fit uncertainties for transition frequencies of less than 150 kHz, with deviations from literature values under 1.1 MHz, limited by pressure uncertainty. This approach has important implications for high-resolution spectroscopy, trace gas detection, and on-chip integration of electro-optic frequency combs.