Must I Pay off a Credit Card That Became Delinquent over 10 Years Ago?

I suspect someone working in the industry "reminded" the company that I did not pay off my balance of $267 over 10 years ago. I lost my job and was unable to pay. I assumed that the balance was written off as bad debt and has since been removed from my credit history. I just received a request for payment on this account in the mail.
Am I legally obligated to pay this unsecured debt now?

Suggestion:

The other answers are MOSTLY correct.

I am not going into the ethical issues here, which are real, but you do not have to pay the debt. However, if you acknowledge that you owe the money, you can in some cases "reinstate" the obligation. Do not call or write to the collection agency to explain anything. Do not say that you know you owed it but you couldn't pay. Do not say that you thought it had been written off. Don't say anything of substance.

Your position should just be that you don't know what they are talking about, but you don't owe anything to anyone. (That part is true. You don't.) If they come forward with the details, your position is still that you don't owe anything on that card. (Still true.) If they press you, just tell them that they are free to sue, but until then you have nothing to say. They can't sue, because of the statute of limitations, and they know that. But don't even mention the statute of limitations, because you could say it in a way that implies you acknowledge the debt. And if you say anything, that admits you have an unpaid bill, you could find out that you suddenly DO owe the money. They are trying to get you to acknowledge and reinstate the obligation. Don't talk to them.