Screwball perfume manufacturer Theresa Lindsay informs George Roberts of the Roberts Advertising Agency that she has decided to change the musical programming of her radio show from Russian to Cuban. Furthermore, Theresa insists that the unknown Desi Arnaz and His Cuban Rhythm Band be imported from Cuba to New York City to star on her show. When the bandleader refuses George's phone and telegram offers, the desperate advertising executive sends Ann Williams, his assistant, to Cuba to personally pursue Desi. She finds Desi and his group working on a plantation on the outskirts of Havana. Desi tells Ann that he refused the radio offer because his sister and brother-in-law were killed in New York City, and that he has been taking care of his orphaned niece Brownie ever since. With Brownie's help and a bit of romance, Ann convinces Desi to go to New York, but he soon becomes disenchanted when he learns that George paid Ann a $5,000 bonus to get him to appear on Theresa's show. Matters are further complicated when Theresa announces that she plans to perform on the radio program with Desi and his band. When Desi refuses to sing with her, Theresa attempts to enlist Brownie's aid by taking the little girl's sick parrot, José, to Alvin, her physician. Instead, Theresa is arrested when the parrot disrupts the doctor's office. Ann then agrees to arrange for Theresa's release from police custody only if the radio sponsor agrees never to sing with Desi. With Theresa at a safe distance, the radio show is a great success, and Desi and Ann are happily united.
