To do this:
Launch the Terminal (Alt + Ctrl + T)
Type the following: mv ~/.config/chromium/Default ~/.config/chromium/Backup
Launch the Chromium again. This time is should open without an error.
Once you have verified it works, close Chromium again.
Go back into Terminal and type: rm -rf ~/.config/chromium/Default
Then type: cp -R ~/.config/chromium/Backup ~/.config/chromium/Default
Exit Terminal and open Chromium and verify your data has returned (bookmarks, etc.)
Once this was solved everytime I started Chromium it would not set as the default browser. I clicked on Set as Default browser and opened Settings > Settings Manager. I clicked on Preferred Applications and on the Internet tab set default web browser as Chromium.
This still didn't work. But with a little help from the Google search engine I found the following fix in Terminal.
mkdir -p ~/.local/share/applications touch ~/.local/share/applications/mimeapps.list