Why is it stuck at v37 when Chromium v39 is already in trusty-updates, for example? Precise is still supported, right? The maintainers are also the same…
The OP is correct, there is no Chromium update to 37 for Precise. This is a known bug and has been reported to launchpad bugs. The stable repository has not been maintained for a few years and adding the "stage" repository will result in upgrading to 48 which won't work on 12.04. As of now this is a problem as 37 is not compatible with the latest libnss3 update and any machine with chromium 37 & libnss3 update can't access google sites or content.
Please have a look at this picture, it says that: Canonical does not provide updates for Chromium:
If you want to get updates for Chromium take this PPA (on Ubuntu 12.04; for other versions go to this page):
sudo add-apt-repository ppa:chromium-daily/stable sudo apt-get update sudo apt-get upgrade
Now you should get a prompt to update Chromium, if it is already installed. if not run this:
sudo apt-get install chromium-browser