Thompson was born into a middle-class family in Louisville, Kentucky, the first of three sons of Virginia Ray Davison , who worked as head librarian at the Louisville Free Public Library and Jack Robert Thompson , a public insurance adjuster and World War I veteran. His parents were introduced to each other by a friend from Jack's fraternity at the University of Kentucky in September 1934, and married on November 2, 1935. Thompson's first name came from a purported ancestor on his mother's side, the Scottish surgeon John Hunter. Hunter Stockton was named for his maternal grandparents, Prestly Stockton Ray and Lucille Hunter. On December 2, 1943, when Thompson was six years old, the family settled at 2437 Ransdell Avenue in the affluent Cherokee Triangle neighborhood of The Highlands. On July 3, 1952, when Thompson was 14 years old, his father, aged 58, died of myasthenia gravis. Hunter and his brothers were raised by their mother. Hunter also had a much older half-brother, James Thompson, Jr., from his father's first marriage, who was not part of the Thompson household. Virginia worked as a librarian to support her children, and is described as having become a "heavy drinker" following her husband's death.

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