In Trimble v. Gordon, the U.S. Supreme Court ruled that an Illinois statute was unconstitutional because it violated the Equal Protection Clause of the Fourteenth Amendment. The law in question prohibited illegitimate children from inheriting property from their fathers unless there had been a court order establishing paternity during his lifetime or if he had married and acknowledged the child as his own before death. Jessie Trimble, an illegitimate daughter, challenged this law after her father's death when she was denied inheritance rights to her father’s estate due to its provisions. The Supreme Court found that while states have broad power over determining inheritance laws, they cannot violate basic principles of equal protection by discriminating against certain classes of people without sufficient justification.

In the dissenting opinion for Trimble v. Gordon, Justice Rehnquist disagreed with the majority's decision to strike down an Illinois law that restricted inheritance rights of illegitimate children. He argued that this was a matter best left to state legislatures rather than federal courts. The justice believed it was not within the Court’s purview to decide on social and economic issues such as these, which he felt were better suited for legislative bodies who are more equipped in dealing with complex societal problems like out-of-wedlock births. Furthermore, he contended that there is no constitutional requirement for states to treat all categories of persons alike; they can make reasonable classifications based on legitimate state interests - here being promotion of familial relationships and stability within family units.