With the recent updates to Moonlight, the newest version now works great in Google Chrome & Chromium. Its pretty easy to get it going..
Download the appropriate CRX file (32 bit or 64 bit) and let it install.
Head over to an MLS Soccer page such as:
… and see if a video works for you. If you get nothing, try right clicking where the video should be, and install the Microsoft Media Pack and once thats finishes, reload the page and videos should work!