We present a method for converting first-person videos, for example, captured with a helmet camera during activities such as rock climbing or bicycling, into hyper-lapse videos, i.e., timelapse videos with a smoothly moving camera. At high speed-up rates, simple frame sub-sampling coupled with existing video stabilization methods does not work, because the erratic camera shake present in first-person videos is amplified by the speed-up. Our algorithm first reconstructs the 3D input camera path as well as dense, per-frame proxy geometries. We then optimize a novel camera path for the output video that passes near the input cameras while ensuring that the virtual camera looks in directions that can be rendered well from the input. Finally, we generate the novel smoothed, timelapse video by rendering, stitching, and blending appropriately selected source frames for each output frame. We present a number of results for challenging videos that cannot be processed using traditional techniques.