Two days ago, I was fired after I was falsely accused of selling a customer list to a competitor. I told my employers numerous times that I did not sell their customer list but they fired me anyway. According to them, after a process of elimination, I was the only one who could have done it. Today I was told by a former co-worker that the competitor told him the list came from information gathered by my former employers and sent to the competitor in 2007 because of a lawsuit regarding breach of contract between the competitor and my former employers. Also today, my former employer and my former co-worker were standing together when they saw me and my former employer said to my former co-worker, "she's the one who sold the customer list."
I am not licensed to practice in Kentucky, so please take my remarks with an extra grain of salt (i.e., the disclaimer that you can't rely on my answer goes doubly).
That being said, it is very likely that the first answer is correct that you don't have a claim for wrongful termination if you were an at-will employee. On the other hand, if you had an employment agreement, including possibly an oral agreement, or were a union member, then you may very well have a claim for wrongful termination. In order to make sure you get the right answer, please do yourself a favor and consult with a local labor and employment attorney.
Another matter that might bear at least a discussion with a local attorney would be any potential claim for defamation if your former employer, or any of your former co-workers, have been telling anyone else that you stole the customer information. Again, I don't practice law in Kentucky so I can't give you a definitive answer, but falsely telling people that you stole protected business information like customer lists and sold them to a competitor is the sort of defamatory remark that could make it harder for you to find other employment. I would caution you that most defamation claims are difficult to prove and can be quite time-consuming and sometimes embarrassing; however, you should at least explore the possibility with an attorney if your former employer has been saying things about you to other people or other businesses.
Employment / Labor Attorney
Kentucky is an at-will employment state, which means that your employer was free to terminate your employment at any time and for any reason or no reason. Employers can even be wrong, and it's not illegal. Sorry I don't have better news.