A group of people from the website, sentintospace.com, did exactly that by sending a weather balloon into space, at an altitude of 50km, and they timed the launch perfectly to capture the shadow of the moon moving across the surface of the earth from a truly astonishing perspective.
According to the team, they filmed the entire thing:
Using a series of cameras aligned with nanometre precision, we filmed 360 degrees of footage for three hours from launch. On landing, we stitched the footage together and digitally stabilised the footage frame by frame to artificially lock the viewer perspective on the horizon, cropping down to a traditional 16:9 ratio. Finally, we speed-ramped the footage to create the world’s first hyperlapse of an eclipse from the edge of space.Sentintospace.com on Youtube
The video is well worth watching!