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We introduce a technique for ultrasensitive absorption spectroscopy using the GHz-rate pulse train from a phase-locked free-electron laser (FEL), in which the fractional power absorbed from one or more laser lines reappears as a signal on the dark background between the pulses emerging from the sample. Preliminary absorption experiments in 15 Torr cm of methane at 3.25mgr;m, using phase-locked pulses from the Mark III FEL, clearly reveal an interpulse beat signal due to absorption by adjacent molecular rotational lines which is generated only in the presence of interpulse phase coherence.