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Unfortunately, unless you have an employment contract which specifically states that you can only be terminated for cause, this is a very dangerous position to be in.
While the CEO's wife may have no legal say in the office, she is the CEO's wife, and if you don't have an employment contract stating that you can only be terminated for cause, you can legally be terminated without cause in your state (called at will employment).
While it would be a HORRIBLE reason for a CEO to terminate someone, simply based on not listening to their wife's ranting, it would not be illegal.
Now, what the wife is doing is technically defamation if she is telling others that you are a liar and if you ultimately lose this job because of her lies, you should absolutely sue her for defamation....but suing while you are still employed hurts more than it helps.
Does your contract specifically state that you can ONLY be terminated for cause?
Otherwise, it is not a real contract. It's just a statement of terms of employment, which is "at will."
Ok, then you're in a better off position. It may be in your best interest to seek local counsel to send her a cease and desist, if you can show that the statements she is make are false AND that she making those statements to someone other than yourself.
If she is just making statements to you, that's not defamation but rather, harassment. You can also seek a cease desist letter there too, but it is just from a different legal angle.
I'm sure that wouldn't warm the CEO up to you, but any termination would be subject to a wrongful termination suit under the contract of employment.