Thanks for the response stgraber. I had to add a comma before the create=file part, or else it would through an error.
lxc.mount.entry = /dev/net/tun dev/net/tun none bind,create=file
Now I have the /dev/net/tun device being created within the container but when I start the openvpn I get the following error:
$ openvpn --config config_file.ovpn
...
ERROR: Cannot open TUN/TAP dev /dev/net/tun: Permission denied (errno=13)
...
tun module loading on host:
$ lsmod | grep tun
tun 28672 0
tunctl output on host:
$ tunctl
Set 'tap0' persistent and owned by uid 0
from within the container (Is this the problem?):
$ ls -l /dev/net/tun
crw------- 1 nobody nogroup 10, 200 Apr 22 00:15 /dev/net/tun