whtsky's wiki

https://www.chromium.org/getting-involved/download-chromium

1. Look in https://googlechromereleases.blogspot.com/search/label/Stable%20updates for the last time "44." was mentioned.
2. Loop up that version history ("44.0.2403.157") in the Position Lookup
3. In this case it returns a base position of "330231". This is the commit of where the 44 release was branched, back in May 2015.(As this build was made at 44 branch point, it does not have any commits merged in while in beta. )
4. Open the continuous builds archive
5. Click through on your platform (Linux/Mac/Win)
6. Paste "330231" into the filter field at the top and wait for all the results to XHR in.
7. Eventually I get a perfect hit: https://commondatastorage.googleapis.com/chromium-browser-snapshots/index.html?prefix=Mac/330231/
8. Sometimes you may have to decrement the commit number until you find one.
9. Download and run!

Typically that's OK, but if you need a true build of "44.0.2403.x" then you'll need to build Chromium from the 2403 branch. Some PortableApps/PortableChromium sites offer binaries like this, due to security concerns, the Chrome team does not recommend running them.