If an at will employee is terminated by their employer for cause and investigation finds that there is no evidence to support the claim, can that employee then sue the employer for wrongful termination given that the employer could not supply evidence to show just cause?

Not being a labor lawyer, normally at will means they can let you go at any time with or without reason, of course there are federal/state laws that may apply to your situation

I am not a lawyer... However,, I was just terminated, I followed policies/procedures, even went to a lawyer==SAD for me after 24 years,, :D... What it really boils down to... What state you live in and the reason for termination... If it was for discrimination of some sort,go to your EEO office... If your short on funds go to your local library and look up the employment laws in your state. You can check your "Legal" system.. you can get free legal advice,, Best of luck to you, :D

I am not a lawyer either. But I thought employment at will means there does not need to be a reason for discharging an employee.

It's not fair, but that's how it is.