Chesney was born as Mary Clark Manion in Randolph County, Missouri, USA, on 3 August 1912, to parents James William Manion (1880–1974) and Gertrude Finnell (1877–1974). She had two older siblings: Finnell Biggerstaff Manion (1907–1987) and Elizabeth Greene (1910–2000). The family lived on a farm in Clifton Hill.

On 15 March 1933, she married Wallace Chesney. The couple had no children. They were married for 63 years, until her husband’s passing in April 1996.

Over the years, Chesney has loved to play cards and sew. She drove until she was 102, and lived on her own until she was 104.

Chesney currently lives in Moberly, Missouri, USA.