I had the same segmentation problem on Ubuntu Mate and after many tries, including downloading from unofficial sources (dangerous) and compiling it myself and I gave up but yesterday I managed to get it to work. I suspect that a new, less buggy version of Chromium has been released (version 55), but here is exactly what I have done.
Do a fresh install of Ubuntu Mate, and immediately reboot. NOTE: If you have the Rpi 3 and use wifi there is a known bug, you must restart the Pi after a fresh install in order to make the wifi available.
Go to System > Administration > Software & Updates. Under “downloadable from the Internet” tick everything. Then under “other software” tick everything (you can leave out source code if you want). Then under “updates” I unticked everything and turned else off because we can update the Pi ourselves with apt-get.
Then in a terminal
sudo apt-get update
Go to the Welcome Screen > Getting Started > Firmware Update
sudo apt-get install raspi-config
sudo raspi-config
In raspi-config go to "Increase file system" and then reboot.
sudo apt-get update
sudo apt-get upgrade
Reboot one last time.
sudo apt-get update
I had an error with auto-updates, it complained about a file (20-auto-updates) or something. I used the file manager (Caja) to move the file it complained about to my home directory with
gksu caja /etc/apt/apt.conf.d/
Go to Software Boutique > Install Chromium.
This loaded & worked fine but video sites like YouTube, BBC iPlayer etc weren't so good, they were almost unwatchable. I am uncertain if buying the codecs from Rpi will fix it as YouTube / iPlayer works fine on OSMC. I am going to try installing the Ubuntu Codecs & non free chromium codecs to see if that makes it better and report back.
chromium --version
anduname -r
(add to your question)