There is no Chairman and the Bureau runs itself. Those deus ex machina orders from the Chairman at the end were actually fabricated by Agent Harry Mitchell.Remember at the end, after climbing higher and higher looking for the Chairman, David and Elise finally make it to the roof of the building and find no one there. Agent Harry then comes upstairs, ostensibly with orders from the Chairman giving David and Elise a reprieve. Harry, the sympathetic rebellious "angel", rather than confirming the Chairman's non-existence or allowing anyone to alter the couple's minds, fabricates an order from the Chairman that lets them go. Compare to Philip Pullman's His Dark Materials.
Harry Mitchell is Satan.Now, hear me out. This is based on the idea of Satan being an agent of God (in movie terms, "The Chairman). Satan, according to many old-world sources both biblical and extra-biblical, is an angel who went against God's plan and possibly gave "secret knowledge" to mortals. Similarly, Harry Mitchell goes against the Chairman's plan and allows a human to have access to the secret world of the Adjusters. This also requires remembering the idea that Satan has a clearly-defined role in the cosmological hierarchy and is not necessarily an evil being (the whole painting Satan/Lucifer/what-have-you as an evil being is a fairly modern, particularly against the scope of history, and western phenomenon).
The film is very loosely inspired by Harrison Bergeron.