Actually YouTube offers it, it’s just not easily found or not documented, I had to try a few things before finding the right URL. Here’s the link for the iframe:
http://www.youtube.com/embed/?list=UUJgvVfUp1e7WTk_5FW7QyAg

Now all channels are playlists, you can get the playlist ID from the “Play All” button in the new channel page (screenshot with cosmic panda)