You may or not have heard that NASA's Next Big Thing will be an asteroid capture mission. They are planning on capturing an asteroid and dragging it back in the Earth zone and putting it into orbit around the Moon so that it can be studied, as explained here in an illustrated article.
Below is a picture of the capture phase of the mission. I can't tell how big the conceived asteroid being captured is supposed to be, but it doesn't look a lot bigger than 20 meters in diameter. I think they should seriously consider catching 2013 GM3. (Maybe this would be a good test of that space debris capure technology the world will be working on. Yeah, right.)