Microwave millimeter/submillimeter wave double-resonance spectroscopy has been developed with the use of technology typically employed in chirped pulse Fourier transform microwave spectroscopy and fast-sweep direct absorption (sub)millimeter-wave spectroscopy. This technique offers the high sensitivity provided by millimeter/submillimeter fast-sweep techniques with the rapid data acquisition offered by chirped pulse Fourier transform microwave spectrometers. Rather than detecting the movement of population as is observed in a traditional double resonance experiment, instead we detected the splitting of spectral lines arising from the AC Stark effect. This new technique will prove invaluable when assigning complicated rotational spectra of complex molecules. The experimental design is presented along with the results from the double-resonance spectra of methanol as a proof-of-concept for this technique.