With the Battle of Portlandia behind him, Chase is a hero now and the rank and file truly believes that he's the prince the Command Team claims he is. For his part, Chase has made his choice and now he's committed. As the face of the revolution he's 'in it to win it' because anything else will lead to his death. The twenty-five million-credit bounty on his head will see to that.
The problem he faces now is convincing Fleet Captain Witner, and his Command Team to trust him, when Chase still doesn't trust them enough to tell them who he truly is. Chase had been betrayed too many times in his past to come clean easily, and for all that he's doing everything they ask of him, until the Captain and his team gives him a seat at the table, he's not about to start trusting any of them.
So he's content to let them continue believing he's a fraud of their own creation to justify the search for a 'real' heir.
Still, he now has Claire on his side, and he can't think of anyone else he'd rather have there. She's as driven as he is, and at least as crazy. He's never met a better fighter and probably never will. As a duchess she's been teaching him valuable lessons about how to act and what to say. As a friend and lover, she's giving him something that he never thought he'd have - a reason to win.