I have a wheezy chroot running on squeeze, using schroot. I'm successfully using Skype. I've installed google-chrome-stable_current_i386.deb (version 38) in the chroot but when I try to run it, it exits immediately and says Aborted. I ran it with strace which indicates this is because it received SIG_ABORT.
When I run google-chrome-stable --disable-setuid-sandbox it works, but complains about stability and security. (Obviously it's using a sandbox for a reason.)
I suspect I'm having the same issue as How do I run chromium inside a chroot?.