In Kitchen v. Rayburn, the United States Supreme Court was asked to decide whether a state court had the authority to issue a writ of habeas corpus to a prisoner who was being held in federal custody. The petitioner, Kitchen, was a prisoner in the custody of the United States Marshal in the Eastern District of Arkansas. He had been convicted of a federal crime and was serving a sentence in the federal penitentiary. Kitchen sought a writ of habeas corpus from the state court, claiming that he was being held in violation of the Constitution. The Supreme Court held that the state court did not have the authority to issue a writ of habeas corpus to a prisoner in federal custody. The Court reasoned that the power to issue such a writ was vested exclusively in the federal courts. The Court noted that the state court had no jurisdiction over the prisoner, and thus could not issue a writ of habeas corpus. The Court also noted that the state court had no authority to review the legality of the prisoner's conviction or sentence. The Court concluded that the state court lacked the authority to issue a writ of habeas corpus to a prisoner in federal custody. The Court held that the power to issue such a writ was vested exclusively in the federal courts.

In Kitchen v. Rayburn, the Supreme Court was asked to decide whether a state court had jurisdiction over an action brought by a citizen of another state against citizens of that same other state. The majority opinion held that it did not have such jurisdiction and reversed the judgment of the lower court. Justice Field dissented from this decision, arguing that there is no constitutional prohibition on states exercising their judicial power in cases involving citizens from other states as long as they do so with due process and equal protection under law for all parties involved. He further argued that if Congress has not specifically prohibited such actions then it should be left up to each individual state to determine how best to exercise its own judicial powers within its borders without interference from outside sources or authorities.