The design of a chirped-pulse Fourier transform microwave spectrometer operating in the 2–8 GHz frequency range is presented. The linear frequency sweep is generated by an arbitrary waveform generator with a sampling rate of 20 GS/s. After amplification, the microwave pulse is broadcast into a vacuum chamber where it interacts with a supersonically expanded molecular sample. The resulting molecular free induction decay signal is amplified and digitized directly on a digital oscilloscope with a 20 GS/s sampling rate. No frequency mixing or multiplication is necessary in this spectrometer, which allows for very high pulse quality and phase stability. The performance of this spectrometer is demonstrated on the rotational spectrum of iodobenzene. All four distinct singly-substituted 13C isotopologues have been detected in natural abundance, as well as two isotopic species of a van der Waals cluster of iodobenzene with a neon atom. Spectroscopic constants and derived structural parameters for iodobenzene and for iodobenzene–Ne are reported. In addition, the use of microwave–microwave double-resonance experiments in this spectrometer to facilitate spectral assignments is presented.Graphical abstractBroadband rotational spectroscopy methods using chirped pulse excitation have been extended to the low-frequency microwave region (2-8 GHz).Highlights► We have built a 2–8 GHz chirped-pulse Fourier transform microwave spectrometer. ► This instrument offers high-sensitivity, dynamic range, and intensity accuracy. ► 13C isotopologues of iodobenzene have been assigned, and its structure determined. ► The microwave spectrum of the iodobenzene–neon complex has been assigned.