Chromium profile prevents chromium-browser from starting (Could not close socketpair: Permission denied)

Can you attach the output of 'grep DEN /var/log/syslog' at the time of the denial?

That denial might be the relevant one:

Sep 26 14:49:10 ubuntu kernel: [ 53.916666] audit: type=1400 audit(1411735750.942:62): apparmor="DENIED" operation="socket_shutdown" profile="/usr/lib/chromium-browser/chromium-browser//chromium_browser_sandbox" pid=2965 comm="chrome-sandbox" family="unix" sock_type="stream" protocol=0 requested_mask="shutdown" denied_mask="shutdown" addr=none

From IRC:
Sep 26 11:42:16 ubuntu kernel: [ 23.300887] audit: type=1400 audit(1411724536.410:59): apparmor="DENIED" operation="socket_shutdown" profile="/usr/lib/chromium-browser/chromium-browser//chromium_browser_sandbox" pid=2921 comm="chrome-sandbox" family="unix" sock_type="stream" protocol=0 requested_mask="shutdown" denied_mask="shutdown" addr=none
Sep 26 11:42:16 ubuntu kernel: [ 23.300914] audit: type=1400 audit(1411724536.410:60): apparmor="DENIED" operation="socket_shutdown" profile="/usr/lib/chromium-browser/chromium-browser//chromium_browser_sandbox" pid=2922 comm="chrome-sandbox" family="unix" sock_type="stream" protocol=0 requested_mask="shutdown" denied_mask="shutdown" addr=none
Sep 26 14:49:10 ubuntu kernel: [ 53.916645] audit: type=1400 audit(1411735750.942:61): apparmor="DENIED" operation="socket_shutdown" profile="/usr/lib/chromium-browser/chromium-browser//chromium_browser_sandbox" pid=2964 comm="chrome-sandbox" family="unix" sock_type="stream" protocol=0 requested_mask="shutdown" denied_mask="shutdown" addr=none
Sep 26 14:49:10 ubuntu kernel: [ 53.916666] audit: type=1400 audit(1411735750.942:62): apparmor="DENIED" operation="socket_shutdown" profile="/usr/lib/chromium-browser/chromium-browser//chromium_browser_sandbox" pid=2965 comm="chrome-sandbox" family="unix" sock_type="stream" protocol=0 requested_mask="shutdown" denied_mask="shutdown" addr=none

It looks like your profile didn't get updated since the chromium profile in the apparmor profile package contains this rule:
    unix (getattr, getopt, setopt, shutdown) peer=(addr=none),

Can you attach /etc/apparmor.d/usr.bin.chromium-browser? (It sounds like maybe you modified this file, upgraded, and chose not to use the new profile. You probably have a /etc/apparmor.d/usr.bin.chromium-browser.dpkg-new that you'll have merge in the changes).

This bug was fixed in the package apparmor - 2.8.96~2652-0ubuntu7

---------------
apparmor (2.8.96~2652-0ubuntu7) utopic; urgency=medium

  * add-chromium-browser.patch: user addr=none instead of peer=(addr=none)
    (LP: #1374363)
 -- Jamie Strandboge <email address hidden> Sat, 27 Sep 2014 07:41:07 -0500