I wanted to try a thematic battle, so I figured I'd take the most Rook City-ish heroes up against the chairman.
I decided that the Rook City team would naturally consist of Wraith, Mister Fixer, and Expatriette. I also added Absolute Zero (he was injured in a Pike lab explosion, and he has a batman-villain feel to him) and Nightmist (she's an occult detective, so I figure close enough).
Five heroes should be pretty easy, but the Chairman is pretty tough, and this team has some weak heroes.
The first match was in Rook City, and the five heroes got stomped. They managed to flip the Chairman, but spent most of their time dealing with underbosses and thugs and never did significant damage to either boss.
The second match was in the Block, which is a much friendlier environement. Also, luckily, the Warden came out on round one, which kept the environement deck largely contained. However, the fight ran long, eventually cycling the Chairman's deck. It was a close fight, with only Absolute Zero and Nightmist standing by the end. The MVPs were Wraith, who used a combo of Utility Belt, Targetting Computer, Razor Ordenance, and Throwing Knives to be the primary damage dealer and Absolute Zero, however, turned into a self-healing damage monster by the end. Mister Fixer and Expatriette never quite found their groove. Nightmist was solid, but spent most of her turns self-healing, but she stopped the Chairman from playing cards a few turns, which helped a lot.
The final match was in the Pike Industrial Complex. This one was interesting because Mister Fixer was the strong point of the team. He got the Pipe Wrench and Monkey Fist in the first draw, and with the nemesis bonus, he just wailed on the Operative. He also drew a Grease Gun and Salvage Yard later, which was fantastic for letting people hammer on the Chairman with impunity. Wraith was a damage engine again. Nightmist did useful support (Mistbound is amazing), and had a solid game. Expatriette got a combat shotgun out early, and did consistent damage, but never really got going. Absolute Zero spent the entire match flailing about, barely accomplishing anything, (particularly when a vat converted all of his damage to Toxic for a while), but he did manage one fantastic card: Subzero Atmosphere. When a late game prison break landed and pulled all five underbosses out of the trash, none of them could summon thugs. As a result, the heroes were saved from taking a pile of Hired Gun damage. Mister Fixer and Wraith then finished off the Chairman, and Expatriette and Nightmist finished off the Operative. All five heroes were left standing, but all have single digit hit points left.