Harrington was born as Mary Agnes Maxwell in Rochester, New York, on 20 January 1889 – some records suggest a birth year of 1887 – as one of five children born to Joseph and Katherine (née McCormick) Maxwell. She grew up on a dairy farm in Clinton, New York.
Harrington married her husband, George, as a young woman. The couple had one son, Donn, in 1912, who was a World War II veteran and died in a plane crash in 1944. Her husband, who worked for a local highway department, died in 1959. Throughout her life, she loved animals, dancing, and entertainer Dean Martin.
Harrington lived independently until the age of 100, when she moved into a retirement home in Utica, New York. She had two nieces, Elizabeth Burns and Dorothy Maxwell, who described her as a private person who suffered from vision and hearing diffculties.
Harrington died on 29 December 2002 at the age of 113 years, 343 days.