This story says that Chicago alderman Byron Sigcho-Lopez, who is an independent candidate for U.S. House in the Fourth District, will file a lawsuit in Illinois state courts to get on the ballot, if the Elections Board keeps him off the ballot.
He would probably have a better chance in federal court. The Illinois state courts are among the least favorable to ballot access, among the state courts of all fifty states. Illinois state courts kept the Harold Washington Party off the Cook County in 1990, but the U.S. Supreme Court reversed that decision. The state courts repeatedly upheld the full-slate law for new parties, but the federal courts invalidated that law in 2016. The state courts have invalidated all statewide initiative petitions since 1980.