A very large reflective surface deployed in orbit around the earth, could in theory, be used to reflect the sun's light down onto the surface of the earth at night. I don't really know how plausible such a device would be, but it does sound possible.
But would it really be feasable to build such a complicated system simply to light up an area at night ? I'm convinced that I've read about plans for building something like this in the past, but nothing like it has ever surfaced. It would certainly be the brightest object in the night sky, thats for sure.