The Gist: A Chinese-American student in Mississippi was not allowed to attend a white-only school because of her descent, even though there were no schools in the district available for the Chinese. The U.S. Supreme Court ruled the school could nevertheless preclude her.
Martha Lum was a 9-year-old citizen of the United States with Chinese blood. During the lunch period of her first day of school at Rosedale Consolidated School, she was told she had to leave and could never come back because she was not white. Gong Lum, Martha's father, brought this case on the grounds that the school's actions violated the 14th amendment.
The 14th amendment states: No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws. Earlier, in Plessy v. Ferguson, the U.S. Supreme Court had determined segregation laws--laws requiring the separation of black people from white people in public facilities--was constitutional because such laws were "separate but equal" (clearly, this was not true, as facilities for white people were far superior). Additionally, in Cumming v. Richmond, the Court expanded this logic by stating local governments could fund a white-only high school without providing an alternative for black people.
Using these cases as precedent, the U.S. Supreme Court held the school's action in precluding a Chinese-American student was legal, and there was no reason why the Chinese-American student couldn't attend a colored school outside of her district. Nor did the Court find any difference between segregation issues involving white and black people and "where the issue is between white pupils and the pupils of the yellow races. The decision is within the discretion of the state in regulating its public schools, and does not conflict with the Fourteenth Amendment."
In essence, the Court held the issue had been settled long ago. This was just another one of many cases (i.e. Minor, Plessy, Cumming, Berea) where the Court gave the 14th amendment minimal value while providing and expanding substantial power to state governments, allowing them great deference to segregate their citizens however they saw fit.
This case was later overruled by Brown v. Board of Education (1954).