Acoustic waves with a wide range of frequencies are generated by lightning strokes during thunderstorms, including infrasonic waves (0.1 to 20Hz). The source mechanism for these low-frequency acoustic waves is still debated, and studies have so far been limited to ground-based instruments. Here we report the first confirmed detection of lightning-generated infrasound with acoustic instruments suspended at stratospheric altitudes using a free-flying balloon. We observe high-amplitude signals generated by lightning strokes located within 100km of the balloon as it flew over the Tasman Sea on 17 May 2016. The signals share many characteristics with waveforms recorded previously by ground-based instruments near thunderstorms. The ability to measure lightning activity with high-altitude infrasound instruments has demonstrated the potential for using these platforms to image the full acoustic wavefield in the atmosphere. Furthermore, it validates the use of these platforms for recording and characterizing infrasonic sources located beyond the detection range of ground-based instruments. Plain Language Summary Lightning generates sound waves across a wide range of frequencies, including below the threshold for human hearing at 20Hz. How these waves at less than 20Hz, also known as infrasound waves, are generated during a lightning stroke is currently an area for debate. So far, measurements of lightning infrasound waves have been limited to microphones fixed to the ground, and models have shown that only a small section of sound waves actually reach the ground. Here we show lightning infrasound that has been detected using microphones suspended over a thunderstorm using a balloon flying at 32km height. This opens up the possibility of using balloons in future studies to make better measurements of infrasound waves generated by lightning activity and, in turn, give a better idea of how they are generated. It also shows how balloons can be used to record infrasound waves far away from land and therefore beyond the detection limit of ground-based microphones.