Sending Network Stream from Playlist (.m3u8) to AirPlay? I have a Mac, an Apple TV, and I have a network video stream (.../stream.m3u8) that I'd like to send over AirPlay to my Apple TV.

If I open it in QuickTime/VLC, it plays great, but neither support streaming video over AirPlay.

And when I try to open the stream in iTunes, it instead adds it as a playlist, instead of playing the video.

I'm aware (and a proud owner) of AirParrot, but it's a "whatever's on your screen" type of thing, which gets a little choppy, and the audio is often not properly synced.

Are there any ways, with a Mac and Apple TV, to send a live video stream over AirPlay, or to open it on my Apple TV?
Well as you said with AirParrot (which btw is also great for Windows users) you can extend your display to a "Specific App…" thus QuickTime/VLC/MplayerX. To avoid choppy video you should use Ethernet cable…
I don't know what can be done and how Mavericks reacts with the second display feature while changing desktop… But I believe you have the same kind of lags.

Air Video HD allows from local device to AppleTV streams : http://www.inmethod.com/airvideohd/index.html
It should not be to complicated to route your favorite remote server on a local IP address /etc/hosts or something like that …

The alternative that would work for AppleTV v2 and v3 (that last one not being jail braked) is to emulate the "Trailers" service to be able to stream from "PlexConnect" :
— http://gigaom.com/2013/06/04/plex-apple-tv-plexconnect/
— http://www.youtube.com/watch?v=H1s09hRaWm4