Idea: "Let's Sing" Facebook app

Writing up a random idea that just occurred to me at three in the morning.

Make a Facebook app called "Let's Sing". I sing any random song into my webcam, then publicly "tag" the next person who must do the same. All resulting videos show up as one long (infinite?) thread. If such an app were available, I'd definitely be a user.

What say ye? I don't know anything about the Facebook platform, is this implementable? Can it fly? Or maybe something similar is already there?