Amy Marcy Cheney was born in Henniker, New Hampshire to Charles Abbott Cheney (nephew of Oren B. Cheney, who founded Bates College) and Clara Imogene Marcy Cheney. Artistic ability appears to have run in the family: Clara was reputedly an "excellent pianist and singer,", and had a sister named Emma Francis "Franc" Marcy, who taught voice and piano in Boston. Emma's daughter Ethel, who "displayed a talent for art," went "to study in New York, Boston, and twice to Paris" during the 1890s. Amy showed every sign of a child prodigy. She was able to sing forty songs accurately by age one, she was capable of improvising counter-melody by age two, and she taught herself to read at age three. At four, she composed three waltzes for piano during a summer at her grandfather's farm in West Henniker, NH, despite the absence of a piano; instead, she composed the pieces mentally and played them when she returned home. The family struggled to keep up with her musical interests and demands. Her mother sang and played for her, but attempted to prevent young Amy from playing the family piano herself, believing that to indulge the child's wishes in this respect would damage parental authority. Amy often commanded what music was played in the home and how, becoming enraged if it did not meet her standards. Amy began formal piano lessons with her mother at age six, and soon gave public recitals of works by Handel, Beethoven, and Chopin, as well as her own pieces. One such recital was reviewed in arts journal The Folio, and multiple agents proposed concert tours for the young pianist, which her parents declined - a decision for which Amy was later grateful. In 1875, the Cheney family moved to Chelsea, a suburb just across the Mystic River from Boston. They were advised there to enroll Amy in a European conservatory, but opted instead for local training, hiring Ernst Perabo and later Carl Baermann (himself a student of Franz Liszt) as piano teachers. In 1881-82, fourteen-year-old Amy also studied harmony and counterpoint with Junius W. Hill. This would be her only formal instruction as a composer, but "[s]he collected every book she could find on theory, composition, and orchestration ... she taught herself ... counterpoint, harmony, fugue," even translating Gevaert's and Berlioz's French treatises on orchestration, considered "most composers' bibles," into English for herself.

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She was able to sing forty songs accurately by age one, she was capable of improvising counter-melody by age two,