Enrica Clay Dillon (1881 – 9 October 1946) was an American opera singer, opera director, and voice teacher.
Born in Denver, Colorado, Dillon was the daughter of Judge Henry Clay Dillon and Florence H. Dillon (née Hood). She was the older sister of composer Fanny Dillon and actress Josephine Dillon; the latter of whom was married to Clark Gable for 6 years.
Dillon studied voice at Mount Holyoke College and with baritone Francesco Mottino in Milan. She had a prolific career as a dramatic soprano in Europe during the first decade and a half of the 20th century, giving more than 1,800 opera performances. She was especially active in Italy and sang at most of the principle houses in that country, including La Scala. She was particularly known for her portrayal of the title role in Giuseppe Verdi's Aida.
Dillon abandoned her singing career shortly before the outbreak of World War I; largely due to continual bouts with illness. She then served as the first director of the Washington Opera Company from 1919 to 1927. She moved to Philadelphia in 1927, where for three years she taught singing and was director of the Philadelphia Operatic Society. From 1930-1935, she worked for Herbert Witherspoon as a vocal coach and stage director at first the Chicago Civic Opera and then the Chicago Grand Opera Company. She also maintained a home in New York City during the 1930s where she had a voice studio and directed operas for the New York Singing Teachers Association and the New York Opera Guild.