James Henry Wright (c. August 13, 1838 – January 17, 1905) was an American jurist and politician. Following his service in the Confederate States Army during the American Civil War, Wright became an attorney in Missouri where he served as mayor of Carrollton and a member of the Missouri House of Representatives. Wright was appointed Chief Justice of the Arizona Territorial Supreme Court by President Grover Cleveland. He served for three years before being removed from the bench by President Benjamin Harrison.