How to run Google Chrome or Chromium on a remote ssh session?

First you need uncomment this lines in /etc/sshd_config on server:

X11Forwarding yes

The second step is connect to server with -X and execute Chromium

ssh -X user@hostname chromium

You will see it on client computer.

Did you try X forwarding option in ssh? ssh -X or ssh -Y, or enable remote desktop service

You are probably missing an X11 Server on the Mac Side. An X11 server used to ship with OS X, but doesn't anymore, however the XQuartz Project provides working client and server libraries and binaries for OS X (even Sierra).

You can run xauth, and export DISPLAY=blah, and xclock all you want, but if you don't actually have an X-compatible display server (and the display on OS X is not X-Windows), it will all be for naught.

XQuartz is also Apple's official recommendation for X on OS X, too.

Once you get XQuartz installed, you should have a much better experience X-Forwarding applications, and at that point some of the other answers in this thread should get you going.