Hamilton was born in Salisbury, Maryland to a physician father who died in a car accident when she was five. Linda has a a twin sister, one older sister and one younger brother. She has said that she was raised in a "very boring, white Anglo-Saxon" family, and "voraciously read books" during her spare time. Hamilton went to Wicomico Junior High (now Wicomico Middle School) and Wicomico High School in Salisbury, Maryland, with her identical twin sister, Leslie Hamilton Gearren. She studied for two years at Washington College in Chestertown, Maryland, before moving on to acting studies in New York City. While attending Washington College, her acting professor told her she had no hope of earning a living as an actress. In The Big Apple she attended acting workshops given by Lee Strasberg.