Mitchell v. United States was a landmark Supreme Court case that dealt with racial discrimination in the military. The case was brought forward by an African American man named Joseph Mitchell, who had been unfairly passed over for promotion in the United States Air Force because of his race.

In 1950, Mitchell filed a lawsuit against the Air Force, arguing that the military's policy of segregating black troops and denying them equal opportunities for advancement was a violation of his constitutional rights. The case made its way to the Supreme Court, where in 1955, the Court ruled in favor of Mitchell. The decision in Mitchell v. United States marked an important turning point in the fight against racial discrimination in the U.S. military, and helped pave the way for greater equality and integration in the armed forces.