I was able to get Teamviewer 10 installed in a chroot of Trusty with Unity (using sudo gdebi teamviewer_linux.deb), however when I attempt to start it it fails with
The TeamViewer daemon is not running! Please start the daemon (needs root permissions) before running.
I attempted to start it by running sudo teamviewer --daemon start and then launching TeamViewer from the dash, but after about 1 second it closes and the daemon seems to have stopped.
Why would the daemon stop in the middle of running TeamViewer?
My final solution was to use Teamviewer 7 for Windows with Wine. It seems versions newer than 7 do not currently work in chroots due to the issue I described in the original question, so 7 is the newest version that does not have this dependency. I use it for remote access and file transfer, so I don't know if all features from version 10 are available, but I can confirm those two are.
If anyone is trying to run Teamviewer within a chroot environment, I recommend simply downloading version 7 for Windows along with Wine and installing it that way.