As a general rule, yes they can. At-will employment in Texas allows an employer to terminate an employee for any reason that is not illegal and is not otherwise a breach of an employment agreement between the employer and employee. And note that an employment agreement is a specific thing – most employees do not have employment agreements, even if they received an offer letter or employee handbook. However, in this situation, it’s possible that the non-compete is not enforceable, depending on whether the employer actually provided “consideration” after making you sign the non-compete. It really, really depends on the facts of the situation. But that’s a different issue than whether the employer can fire you for not signing. The Texas Supreme Court has said that an employer’s threat to fire an employee is not sufficient coercive to invalidate certain employment agreements that an employee signs to avoid termination. (Yes, really.)