Dr. David Huxley, a mild-mannered paleontologist, eagerly awaits the arrival of a crucial dinosaur bone for his museum's brontosaurus skeleton, while also preparing for his imminent marriage. His life takes an unexpected turn when he encounters Susan Vance, an eccentric and capricious heiress, who causes a series of mishaps beginning with her accidental stealing of his golf ball during a charity event. Susan's chaotic influence only intensifies when she convinces David to help her transport her pet leopard, Baby, who is a gift for her aunt. Their adventure turns more absurd as the leopard escapes, leading to a string of comic misunderstandings and increasingly entangled predicaments.

As David reluctantly gets further embroiled in Susan's whimsical escapades, their journey becomes entangled with stolen cars, mistaken identities, and run-ins with an assortment of quirky characters including Susan’s exasperated aunt and a befuddled sheriff. Amidst the chaos, David navigates through a whirlwind of confusion and hilarity, struggling to keep his professional and personal life intact. With plans constantly thwarted by Susan's antics and the unpredictable behavior of Baby, he finds himself questioning his priorities and the path he thought he was on. The narrative propels towards a climactic series of events that reevaluate perceptions and lead characters to unforeseen changes in their lives.