Does Last.fm support mean just scrobbling, or are there other features you might like? I'm not a Last.fm user but I'd be willing to take a look into including support down the road!
Last.fm scrobbling was the first thing I looked for as well. It's pretty much a necessity for me at this point that any software-based music player I use needs to support last.fm scrobbling. There's several Chrome extensions that take care of it for the in-browser player as people below have mentioned.
I just fired this up, it looks and works great! If you did implement last.fm scrobbling (currently I just use a tampermonkey script that works well) I'd start using it primarily.