[rwg]

You need to talk to a lawyer who specializes in Texas employment law ASAP. Do not sign anything that you do not fully understand the implications of, even if your reading of the non-compete agreement and Texas's Covenants Not to Compete Act makes you think the agreement is completely unenforceable.

While you're talking to the lawyer, don't forget to ask if the non-compete agreement is still in effect in the event you're "involuntarily separated" (sacked, with or without cause) from the company. The answer may greatly influence your decision.

Finally, as is mentioned elsewhere in the comments here, do not sign anything because random HR person says whatever you're signing is never really enforced. HR does not work for you, and "but so-and-so in HR said..." is not a strong defense against your signature on a contract. If the non-compete is never enforced, then the company should have no problem with you not signing it.