You can go through the Penal Code, specifically Chapter 46 (weapons) and Government Code Chapter 411 (which establishes CHL) from one end to the other. Nowhere does it say that it is illegal to carry with a round in the chamber.
You can either legally possess a weapon or not. It does not matter whether it is loaded or even capable of firing.
I have found that the best solution for people like this is to ask them to show you where what they are saying is against the law. Then let them bathe in the warm bathwaters of ignorance.
Many states do prohibit carrying loaded weapons in many circumstances, and the federal "gun free school zone" law also includes that aspect -- but not Texas law.
- Jim