Chase began to study art in 1869 at the National Academy of Design, New York. In 1872, Chase set off for Munich. He registered at the Royal Academy and spent the next six years studying and traveling. Chase returned home to New York in 1878 and taught at the Art Students League. He rented a studio in the 10th Street Studio Building, a space he was to keep until 1895.
Chase was elected a member of the National Academy in 1890. He began to spend more time teaching, founding the Shinnecock Summer School of Art on Long Island, New York, in 1891. Chase offered courses through the Brooklyn Art Association, the Art Institute of Chicago, and at his own Chase School of Art—later known as the New York School of Art.
The last years of his life Chase received many honors, including medals at the 1900 Paris Universal Exposition, the 1901 Buffalo Pan-American Exposition, the 1904 St. Louis Universal Exposition, and the 1910 Buenos Aires International Fine Arts Exposition.