“Miss Sloane” is meant to be an “Insider”-like expose of lobbying by way of the controversy over a gun control bill, and while director John Madden (“Shakespeare in Love,” “Proof”) and writer Jonathan Perera deliver some hard blows on both the gun lobby and lobbyists in general, the film is most noteworthy for two terrific female performances. The first is the star turn by Jessica Chastain as the titular Miss Sloane, who is an all-work, no play lobbyist who has abandoned a cushy job at her previous employer for a position working for the Brady lobbyists who have been pushing for gun control, to no avail, for years. The second is Gugu Mbatha-Raw (“Belle”) as Esme Manucharian, a number cruncher and fact-checker for the gun control advocates who develops a bond with Elizabeth Sloane. She wonders why someone like Sloane, who knows all the tricks to lobbying successfully, would take on what appears to be a losing battle. She assumes there’s a personal reason, but no, Sloane says she believes in the cause and the efficacy of the arguments for it. That said, even she knows that it’s an uphill climb to get enough Senators to vote yes against the most powerful lobby in Washington, despite support from the public. That divide between what the people support vs. what lobbyists want is one of the key points in the movie, likely inspired by the 2013 fight for universal background checks after the Newtown shooting in 2012, but what really powers it is watching Chastain’s character as she shares her knowledge on lobbying in Washington with people who are fundamentally good-natured, and wonder why the arguments they make aren’t persuasive enough. The film’s primary framing device is Sloane in front of a Senate Ethics Committee for her legally dubious practices, but without Chastain, in full “Zero Dark Thirty” mode of determination, the film might be a flat drama that would be little better than your average movie-of-the-week on the subject. With her and Mbatha-Raw, it’s a fascinating study of the ways an issue gets debated in Washington, even if it’s a sobering reminder of why some debates are destined to fail.