Chirped-pulse Fourier transform spectroscopy has recently been extended to millimeter wave spectroscopy as a technique for the characterization of room-temperature gas samples. Here we present a variation of this technique that significantly reduces the technical requirements on high-speed digital electronics and the data throughput, with no reduction in the broadband spectral coverage and no increase in the time required to reach a given sensitivity level. This method takes advantage of the frequency agility of arbitrary waveform generators by utilizing a series of low-bandwidth chirped excitation pulses paired in time with a series of offset single frequency local oscillators, which are used to detect the molecular free induction decay signals in a heterodyne receiver. A demonstration of this technique is presented in which a 67 GHz bandwidth spectrum of methanol (spanning from 792 to 859 GHz) is acquired in 58 μs.