HB 2756, the bill that would have allowed CHL holders to open carry didn’t make it to the calender for this session and is effectively dead. The bill was a long shot since the TSRA didn’t support it* and it didn’t allow anyone to open carry unless they had a concealed handgun license.
(Thanks to Joseph Kerr for the update in comments here.)
The next legislative opportunity for open carry in Texas will be in 2013.
*I still haven’t heard a good explanation why the TSRA doesn’t support open carry. I’ve been told “it’s not a priority” or “the members don’t support it” but I’ve also heard that the CHL training establishment is very much against open carry since it would presumably hit them in the wallet. Regardless, the TSRA did NOT support HB 2756.