I have a solution! At least, it seems I do.
I'm running Ubuntu MATE 16.04 on an ODROID XU4 board. Really capable little machine. Except that I couldn't get Chrome to sign-in - giving the infamous "Uh-oh!" error. Now, seeing Chrome 53 working, it seems that there's a new interface for authenticating, which may be why it fails. In my build, Chromium's packages were held-back by default, stuck at an old build (48, I think). Unlocking it resulted in the "Segmentation Fault" error discussed in this thread. Going through a couple hunches and some leads here, I finally found a combination that works.
Problem is, I'm a "new user" so I can't post links... I'll have to obfuscate these (the terminal commands will need to be edited).
Anyway, here's what I did to get Chrome 53 working on it.
1) Go to http://ports.ubuntu.com/ubuntu-ports/pool/universe/c/chromium-browser/ and locate the Chromium packages for Ubuntu 14.04, not Ubuntu 16.04. In my case, these were:
2) Install these packages using "dpkg -i"
3) Hold the packages, if desired, to prevent an "apt-get upgrade" from overwriting with bad versions.
In plain English, summary to get you on version 53:
Open a Terminal
Enter the commands (edit the "hxxp" since I "can't post links"!)
Now, you'll need to sudo, so you can't paste commands all at once (it'll enter pasted data as your password). So, start with one sudo that'll give you a session:
sudo dpkg -i chromium-codecs-ffmpeg-extra_53.0.2785.143-0ubuntu0.14.04.1.1145_armhf.deb
Then, once that is done, run this:
sudo dpkg -i chromium-browser_53.0.2785.143-0ubuntu0.14.04.1.1145_armhf.deb
sudo dpkg -i chromium-browser-l10n_53.0.2785.143-0ubuntu0.14.04.1.1145_all.deb
sudo apt-mark hold chromium-browser chromium-browser-l10n chromium-codecs-ffmpeg-extra
That should be it! However, one last thing I did along the way that may or may not be necessary - one fix I attempted (that got Chromium 50 working) was to also install libgcrypt11_1.5.3-2ubuntu4.3_armhf.deb. You may need to look that package up and install as well. Would love to know if it's necessary with the steps above.