This worked for me to get chrome to use osmesa
sudo apt-get install libosmesa
sudo ln -s /usr/lib/x86_64-linux-gnu/libOSMesa.so.6 /opt/google/chrome/libosmesa.so
google-chrome --no-first-run --user-data-dir=~/chrome-stuff --use-gl=osmesa
Warning: When running with osmesa the entire page is rendered with osmesa making it pretty slow. So, if there are tests you have that can run without WebGL you probably want to run them without osmesa.
Also note that chrome itself uses osmesa to headless test but it uses a specific version. At the time of this answer it was version 9.0.3. It also makes a few changes listed here
Otherwise to run headless in general I found this
https://gist.github.com/addyosmani/5336747
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