I had the exact same problem, and had come to the conclusion that Chromium had been abandoned. In any case, when the Unity Webapps Preview was released I installed it right away, and it updated both FireFox and Chromium. After FireFox moving so slowly it hurt, I moved back to Chromium and decided I could live with it being outdated... Lo and behold! It had been updated!
To install the Webapps Preview:
sudo add-apt-repository ppa:webapps/preview
sudo apt-get update
sudo apt-get install unity-webapps-preview
Wait for everything to install, and Chromium should be fully updated:
If you don't want to use the Webapps, then you can just go to Chromium's extension page and select to disable the add-on:
If you want to uninstall Webapps:
sudo apt-get install ppa-purge
sudo ppa-purge ppa:webapps/preview
N.B. Using ppa-purge removes all the packages that were installed or upgraded by the ppa you added: this means that Chromium and FireFox (as well as other applications) will be downgraded. If you use Chromium's sync function, this will cause an error when you start the program telling you that your profile is from a newer version of Chromium, and that you should upgrade or change profiles.
Hope this helps!