Wrongful termination? Hiring before firing?

What is the name of your state (only U.S. law)? Maine

I was fired and two days later someone else (a previous employee) filled my position after moving back to the area. Do I have a legal case here? Would the labor board of Maine be on my side?

First the hiring and the firing may have been independent incidents.

Second, it doesn't matter if they were or not.

It is not illegal to fire one employee so that you can hire one you like more.

There is no state where you have automatic rehire rights.

What reason were you given for the firing?