Can you clarify exactly what you see when you open Chromium? Does the window appear on screen at all? Can you use it as normal for the few seconds before it crashes? Does the window just disappear?
Please try closing all Chromium windows, then opening Terminal, and running:
Does this work any better?
I see this in the log:
jan 15 17:29:04 endless chromium-browser.desktop: [3484:3484:0115/172904.670597:ERROR:gpu_process_transport_factory.cc(967)] Lost UI shared context.
jan 15 17:29:05 endless chromium-browser.desktop: [3484:3484:0115/172905.719014:ERROR:x11_input_method_context_impl_gtk.cc(144)] Not implemented reached in virtual void libgtkui::X11InputMethodContextImplGtk::SetSurroundingText(const base::string16 &, const gfx::Range &)
jan 15 17:29:06 endless chromium-browser.desktop: [3484:3600:0115/172906.822211:ERROR:nss_util.cc(748)] After loading Root Certs, loaded==false: NSS error code: -8018
but I see the second and third lines on my system too, and Chromium seems to work fine.