Hillis was born in Kokomo, Indiana in 1921. She began studying the piano when she was 5, and by the time she was 8 she dreamed of becoming a conductor. She was multi-talented, with a wide range of personal accomplishments. As a civilian flight instructor, she taught Navy pilots in World War II. She won golf championships as a young amateur player and was an accomplished musician, playing a range of instruments in high school. She studied music composition at Indiana University and choral conducting at the Julliard School.
Early on Hillis recognized the gender bias that existed for women who wanted to be orchestra conductors and focused her energies and talents on creating great choral music. Under the tutelage of Robert Shaw and Julius Herford, she gained fame as an innovative, creative director and conductor. Hillis was brought to Chicago in 1956 by Maestro Fritz Reiner to establish the Chicago Symphony Chorus. Over the course of her thirty-seven years in that capacity, she prepared the Chicago Symphony Chorus for forty-five recordings with the Chicago Symphony Orchestra. Nine of those recordings were awarded with a Grammy from the National Academy of Recording Arts and Sciences. Hillis captured nationwide attention on October 31, 1977 when she substituted on short notice for the ailing Sir Georg Solti, conducting the Chicago Symphony Orchestra and Chorus in a performance of Gustav Mahler's Symphony No. 8 at New York's Carnegie Hall.
Hillis was the music director and conductor of the Elgin Symphony Orchestra for 14 years, transforming the orchestra from an amateur group to one that was almost entirely professional by the end of her tenure. Her protégé, Dr. Robert Hanson then conducted the ESO until his retirement in 2011. Her ongoing legacy continues with the current ESO Music Director Andrew Grams. He, like Hillis, studied at the Cleveland Symphony Orchestra under Otto Werner Mueller.