WASHINGTON  The Supreme Court on Tuesday agreed to hear an appeal from Jeffrey K. Skilling, the former Enron Corporation chief executive who was sent to prison in 2006 for his role in the company’s spectacular collapse.

Mr. Skilling argued that a law under which he had been convicted was unconstitutionally vague and that he had not received a fair trial in Houston, the city where Enron was based and which bore the brunt of its demise.

The law Mr. Skilling challenged makes it a crime to “deprive another of the intangible right of honest services.”

Federal prosecutors have used the law to combat public corruption and fraud by corporate officials. The law does not require prosecutors to prove theft of money or property but only that defendants have been disloyal to or dishonest with their constituents or employers.