On July 29, 1939, renowned British big game hunter Captain Alan Thorndike (Walter Pidgeon) slips through the forest undetected near the Berghof, Adolf Hitler's residence near Berchtesgaden. Getting the dictator in his telescopic sight, he pulls the trigger on his unloaded rifle and gives a wave. He ponders a moment, then loads a live round, but is discovered at the last second by a guard, and the shot goes wild.
After being beaten up, Thorndike is taken to Major Quive-Smith (George Sanders). Quive-Smith is also a devoted hunter and an admirer of Thorndike. Thorndike explains that it was a "sporting stalk", not to kill, but just for the thrill of going after the biggest game of all. The Nazi half-believes him, but insists he sign a confession that he was in fact working for His Majesty's government. When Thorndike refuses, he is tortured, but remains steadfast and warns of "questions being asked in high places" if he is killed, as his brother, Lord Risborough (Frederick Worlock), is a very important diplomat. The phrase gives Quive-Smith the idea to have Thorndike thrown off a cliff to make his death look like an accident.
Thorndike survives when his knapsack gets caught in a tree, breaking his fall. He eludes his German pursuers and reaches a port. He steals a rowboat, but is forced to abandon it hastily when a patrol boat comes near. He swims to a Danish ship about to sail for London. Vaner (Roddy McDowall), the English cabin boy, helps Thorndike hide. The Germans find Thorndike's coat and passport aboard the rowboat and search the nearby ship. Though they find nothing, they place agent Mr. Jones (John Carradine) on board using Thorndike's passport to continue looking even after the ship leaves the harbour.
Jones is met by German agents in London. Thorndike, mistakenly believing he is now safe, casually debarks and is spotted. He manages to shake off his pursuers by ducking into the apartment of Jerry Stokes (Joan Bennett), a young woman. Jerry lends him money so he can reach his brother.
When Lord Risborough tells his brother that the British government, continuing its pre-war policy of appeasement, would have to extradite him if he were found, Thorndike decides to hide in Africa. Jerry tries to refuse a large cash reward, leading Lady Risborough (Heather Thatcher) to assume that it is payment for other services, but Thorndike insists. He also buys her a new hatpin, as she had lost hers when they first met. She chooses a cheap chromium arrow and insists Thorndike present it to her. Thorndike likens it to her, saying both are "straight and shiny". By this point, Jerry is in love.
Quive-Smith arrives in London to join the hunt. When Thorndike calls on his solicitor, Saul Farnsworthy (Holmes Herbert), the Nazis are once again on his trail. Chased into a London Underground station, Thorndike struggles with Jones, who is killed when he is thrown onto an electrified rail.
Thorndike tells Jerry to have Lord Risborough send him a letter in three weeks time care of Lyme Regis Post Office. As in the novel, Thorndike hides in a cave. However, when he goes to pick up the letter, the postmistress (Eily Malyon) seems alarmed and sends a girl on an errand. Thorndike grabs the letter and beats a hasty retreat. Back at his cave, he finds the letter is from Quive-Smith, who has followed him to his lair.
Quive-Smith seals the only entrance and passes his quarry the confession and a pen through an air hole, threatening to leave him trapped inside. Quive-Smith also slides in Jerry's beret with the arrow pin, informing Thorndike that she was thrown out a window to her death when she would not betray him. They only discovered Thorndike's location through the address he had written down for her. Badgered by the Nazi, the grief-stricken Thorndike finally admits that he subconsciously intended to assassinate Hitler after all. He then agrees to sign the confession. Quive-Smith unblocks the entrance, but waits to shoot him as he crawls out. Thorndike however has other plans; he uses his belt, a slat from his bed, and a stick to fabricate a bow, using Jerry's pin as the tip of a makeshift arrow, and shoots the German through the air hole. When Thorndike emerges, Quive-Smith manages to wound him before dying. By the time Thorndike recovers, the war has started.
Thorndike joins the R.A.F. as a Bomber Command crewman. On a mission over Germany, Thorndike unexpectedly parachutes into the Reich with his hunting rifle to finish what he had started.