Can appellate heavyweight Andrew Pincus of Mayer Brown revive the Delaware Chancery Court’s scheme for resolving business disputes behind closed doors?

In a 134-page brief filed by Pincus on Tuesday, all five Chancery Court judges asked the U.S. Court of Appeals for the Third Circuit to reverse an earlier ruling that Delaware’s confidential business arbitration program is unconstitutional. A nonprofit called the Delaware Coalition for Open Government (DelCOG) challenged the program on First Amendment grounds and persuaded a federal judge in Philadelphia to nix the shadow court earlier this year.

In hopes of cementing Delaware’s place as a prime venue for commercial litigation, the state’s legislature enacted the government-sponsored arbitration program in 2009 and appointed Chancery Court judges to serve as arbitrators. At least five companies have availed themselves of the program, which promises total confidentiality and a streamlined alternative to traditional Delaware court proceedings.

DelCOG first filed its case in U.S. district court in Wilmington in October 2011, alleging that the program violates the public’s right to court access. The Chancery Court hired Wilmington-based Bouchard Margules & Friedlander for its defense, along with Widener University School of Law professor Lawrence Hamermesh.

U.S. District Judge Mary McLaughlin in Philadelphia, sitting by designation in Wilmington, iced the arbitration program in an Aug. 30 opinion. “[T]he Delaware proceeding functions essentially as a non-jury trial before a Chancery Court judge,” she ruled. “Because it is a civil trial, there is a qualified right of access and this proceeding must be open to the public.”

Pincus, who declined to comment on Wednesday, was brought in by the state in to argue the Chancery Court’s Third Circuit appeal. “Additional counsel was sought to address the issues on appeal and, after considering various options, Mayer Brown was retained to assist with the appeal,” a spokesperson for Delaware governor Jack Markell told us.

We named Pincus Litigator of the Week back in April 2011 when he won the landmark U.S. Supreme Court ruling in AT&T v. Concepcion, which upheld the legality of certain class action waivers. Pincus, who’s argued 23 cases before the Supreme Court over his career, is also well-known for helping defend Chicago mayor Rahm Emanuel’s right to run for office.

Our sister publication Delaware Business Court Insider has a good run-down of Pincus’s arguments in Tuesday’s Third Circuit brief. The Chancery Court’s primary contention is that McLaughlin ignored the “experience and logic” test that was enshrined by a nearly 30-year-old Supreme Court ruling in Press-Enterprise Co. v. Superior Court. In that case, the high court held that there’s a First Amendment right of access to a court proceeding only if the proceeding has traditionally been open to the public and if open access would logically enhance the fairness of the proceeding. By eschewing the experience and logic test, the Chancery Court argued, McLaughlin’s decision “introduces tremendous subjectivity and uncertainty into the First Amendment inquiry.”

On deck for DelCOG at the Third Circuit is David Finger, an attorney at Wilmington-based Finger & Slanina and an advocate for open government who helped found the non-profit back in 2006. We named Finger Litigator of the Week in September when he prevailed at the district court. Finger wasn’t immediately available to comment on Wednesday other than to confirm that he’s singlehandedly countering the Chancery Court’s appeal.