I was recently offered a salary position in Louisiana on 1-28. The position had a start date of Monday 2-12. The offer letter, which was signed and returned, included verbage that relocation from South Carolina would be covered by the company.
In preparation for the move to Louisiana, utilities companies (power, cable, telephone, etc) were contacted for termination. I also had 5 months left on an apartment lease, as well.
I then received a written notice on 2-9 that the offer has been rescinded without explanation.

What legal recourse do I have?

Possibly none. It depends on the specifics surrounding the rescinding.

As an example, I once worked for a company that had to rescind the offers we'd made to a half-dozen people when we had fully half our funding pulled out from under us through no fault of our own and with no notice whatsoever. In addition to rescinding outstanding offers, we had to lay off no less than half our staff including vitally needed personnel. In those circumstances, the law was not going to hold us liable since we had no more control than the applicants did.

On the other hand, if the rescinding was done due to someone's error or carelessness, you might have some recourse.

You'll need to talk to a local attorney about your options.

You'll need to talk to a local attorney about your options.

Yep, it stinks that you had an offer and incurred expenses to make the move that won't happen.

cbg's advice is sound.