The Philco Television Playhouse S01E21 - Twelfth Night

Viola, a young woman who disguises herself as a man to work as a page in the court of Count Orsino. Orsino is hopelessly in love with a woman named Olivia, and soon Viola finds herself hopelessly in love with Orsino. But Orsino thinks she's a man, and her predicament worsens when she realizes that Olivia has fallen in love with her.