Plot for THE BIG CHASE has Korean-War vet Grayson returning from that Police Action and joining the L.A. Police Academy, which we learn in a flashback told by Police Lt. Ned Daggert (Douglas Kennedy) to story-hunting reporter Milton Graves (Joe Flynn as Joseph Flynn.) We also learn that Pete's wife Doris is in a family way and eight months or so along, and she is worried because her doctor (Wheaton Chambers) has told her she is anemic---and this must be an internal condition, because Adele Jergens was never anemic---but this doesn't keep her from lighting up a cigarette and downing her anemic pills with a shot of bourbon. No, this was a 50's thing and was not intended as some kind of PSA about the dos-and-donts of being pregnant.
Meanwhile, over to the state pen, where Brad Bellows (played by Davis and not named Brad Meggs as shown on site) and Jim Meggs (played by Jay Lawrence and not named Jim Bellows, as shown on site) are planning a big heist as soon as Brad gets out of prison and has six months to plan this caper. As executed, the caper appears to have been planned in six seconds. Meanwhile, Doris frets over the safety of her husband on his appointed rounds and worries about her anemia and smokes some more cigarettes to help her bridge her current problems, although the chances she may give birth to a pea head if she doesn't lay off the nicotine doesn't occur to her, since the Surgeon General hasn't yet got around to screwing up the beautiful cigarette-package labels with those unsightly warning labels that came later.
Okay, enough plot set-up. Bellows and Miggs and Kitty, who is Bellows wife but wimpy motel-owner Phil Arnold thinks she is his wife and space does not allow the telling of this segment of the story as it is the one highlight of the total film, or films if you insist. And, riding in the back seat of the stolen convertible is none other than Lon Chaney Jr., who, despite the fact he is third-billed, has only about ten minutes of footage to go with his zero lines of dialogue, unless a grunt or two counts as dialogue. They rob a payroll-truck and take off in their stolen car, and wheel down the Hollywood Freeway and are soon spotted by Grayson and his Car-22 partner, and the big chase part of THE BIG CHASE now commences. Kitty, the designated driver, is shot during this pursuit, although Chaney is directly between her and Grayson's line of fire, and the curved path this bullet takes is akin to the path of the 1963 Magic Bullet in Dallas and should disarm those conspiracy nuts who think a bullet can't dart and dodge here and there.
Davis, from the passenger side, guides the car to a halt down at the S.P. yards, and there is a lot of running around, over, between and under some S.P. box cars and even a shot of a slow-moving train engine about to run over the 3-D audience even it does lose a bit when Warrenton's camera is jerked sideways. Chaney gets his at the RR yard, and while he is getting his, Bellows and Miggs hotfoot it over to some other L.A. neighborhood and steal another car and it is about this point that one begins to question just how much time Bellows really put into planning this caper. And they get clean away or would have if the motel owner who thought he was married to Kitty hadn't gotten P.O'ed when he learned that Bellows had dumped the body of his ex-non wife into the La Brea tar pits, and tells all. So Daggert radio's Grayson and tells him the plan and he needs to get over to some park somewhere where a helicopter is waiting for him. The next shot shows the two pursue-es slogging across a beach to get to a rowboat. Yes, a rowboat. They row this boat out about fifty miles to where there is a motor boat moored to a buoy. They board the motor boat and head for an island---which it appears is why they called the 3-D short BANDIT ISLAND---and it is never revealed just what mode of transportation Bellows had chartered to escape from the island on, as Grayson, now really mad about Bellows shooting his prop-dummy sidekick, supplied by Props Master Ernie Johnson, has landed. And, soon after some more 3-D scuffling and camera-ducking, the 3-D part that isn't in 3-D anymore, ends and we get back to the hospital where Adele Jergens has delivered a bouncing, healthy---one can hope---baby girl and is frettin' because she hasn't provided her husband with a bouncing baby boy, but he tells her it is okay, as one of the next 15 is bound to be a boy...and she reaches for her pack of Camels.