The way “The Debt” is structured, it’s as if audiences get two movies in one: a late-’90s-set spy movie with its mid-’60s prequel already attached, both roughly an hour apiece. In the ’90s half, essentially the wraparound story, Mirren plays Rachel Singer, one of three Mossad agents who, in the ’60s half (when she’s played by Jessica Chastain, “The Help”), hunkered down in a dingy Berlin apartment to track down a German gynecologist (Jesper Christensen, “Quantum of Solace”) wanted for Nazi war crimes.

I won’t spoil what Madden quiet effectively keeps secret from moviegoers until their need-to-know point, somewhere after the halfway mark, even if plot summaries and marketing materials do. The colder you are going in, the richer your experience will be. After all, how often does a spy movie with an Oscar winner rely more on story than shrapnel and sex?

The script — written in part by “X-Men: First Class” director Matthew Vaughn, remaking the 2007 Israeli film “Ha-Hov” — presents itself in a nonchronological manner at first, so confusion over the dual time periods’ counterparts may have you scratching your head for a bit. Don’t worry: It’s only for a bit — all is cleared up by the time the plot requires it to be.

While Mirren is front-and-center on the poster and in the credits, “The Debt” really belongs to Chastain, who’s quite remarkable. So compelling is her role in the mission, that I wish the film were all about that. She has some scenes opposite Christensen, where she visits his practice under the guise of being unable to conceive — that’ll make you cringe. In a good way, of course. —Rod Lott