Stratospheric high-altitude balloons (HABs) have great potential as remote sensing platforms for Earth observations, complementing orbiting satellites and low-flying drones. At altitudes of 20–35 km, HABs operate significantly closer to the ground than orbiting satellites but significantly higher than most drones. Therefore, HABs offer unique potential for high-spatial-resolution imaging with large-area coverage. Two other imaging parameters important for Earth observation applications are spectral resolution and spectral range. Hence, in this work, we present the development and testing of a hyperspectral imaging system capable of recording near-video-rate images in narrow contiguous spectral bands from a HAB platform. In particular, we present the first stratospheric environmental tests and HAB flight of a snapshot hyperspectral camera based on computed tomography imaging spectroscopy, which is well-suited to address the challenges posed by the motion of the HAB platform and stratospheric environment. We successfully acquired images with the system under both simulated stratospheric conditions in the Mars Simulation Laboratory at Aarhus University and a 5-h HAB flight mission named HEIMDAL from Kiruna in October 2024 as part of the REXUS/BEXUS 34/35 2024 campaign organized by DLR-SNSA. This study represents a step toward deploying the HAB platform for high-quality land-cover classification.