Sleep with the bike if you have to. Thieves are more determined than you give them credit for, I live on a college campus and everyone i know (not an exaggerations) has had a bike stolen at one point, all have been locked up at the time, and trust me when I say they were not all nice bikes, I actually don't think one was a nice bike. Now onto the next subject, Water is the mortal enemies of bikes, you seem to just be worried about the chain but there is a lot more to the bike that is going to hate the water than just the chain, most everything is filled or containing some type of oil or grease, getting water in there, will compromise the lube around your bearings and everything, and if its not a really nice bike there is a decent chance not everything is sealed. If you do leave it outside cover it completely, but I would recommend giving up your floor before leaving your bike outside if you care about it at all. If that doesn't sound like you take your beater bike instead.