Background:
In 1777 troops stationed in Georgia were short on supplies. The state of Georgia authorized the procurement of supplies from a South Carolina merchant named Robert Farquhar. The state of Georgia never paid for the supplies. After Farquhar died his estate brought suit against the state of Georgia in federal court. The district court dismissed the case on grounds that a state cannot be sued by a citizen of another state.
After the dismissal Chisholm filed the suit before the Supreme Court. A representative from the state of Georgia did not appear. The court decided to hold the case over until 1793 so Georgia could provide representation. Georgia did not send representation in 1793 either and the court proceeded to hear the case.
The court analyzed 4 questions including whether or not a State could be sued by a citizen of another state. The justices who heard the case were Chief Justice John Jay, and associate justices William Cushing, James Wilson, John Blair, and James Iredell. The decision was reached 4-1 with Iredell dissenting ruling that Georgia could be sued. As a result the 11th amendment was passed in 1795.
Opinion: https://www.law.cornell.edu/supremecourt/text/2/419