There doesn't seem to be an easy way to do this. I first thought the following steps would solve the problem, but alas no!
- Download and install Google Chrome v40.0.2214.91 from http://google-chrome.en.uptodown.com/mac/old
- In Applications, CTRL-click on the Google Chrome icon and select Show Package Contents
- Go to /Contents/Versions/40.0.2214.91 which contains Google Chrome Framework.framework
- In the Finder, change to list view if you haven't already, so that you can see which files and folders are contained in the above framework
- Copy the file ffmpegsumo.so from the Libraries folder and paste in the the corresponding folder of your Chromium app
- Uninstall Google Chrome
- Restart Chromium
I have found that some users have been successful using the Chromium Embedded Framework. Follow this link to head to a post on the forum detailing how to build CEF with support for proprietary codecs (namely H.264 and MP3).
On Mac, prior to building CEF by running the automated script automate-git.py, open the Terminal and set the GPY_DEFINES variable as follows:
export GYP_DEFINES="proprietary_codecs=1 ffmpeg_branding=Chrome"
Instructions explaining how to build the CEF may be found here.