Final answer:
Thurgood Marshall was famous for arguing the case of Brown v. Board of Education before the Supreme Court. The case challenged segregation in public schools and led to the Court ruling that segregation was unconstitutional.
Step-by-step explanation:
The case that Thurgood Marshall was famous for arguing before the Supreme Court was Brown v. Board of Education. In this landmark case, Marshall represented the National Association for the Advancement of Colored People (NAACP) and the Brown family. The case challenged segregation in public schools and ultimately led to the Court ruling that segregation was unconstitutional.