Azro Eugene Cheney was born in Ashtabula County, Ohio on April 15, 1854. His parents, Harvey Cheney and Julia Ann Everts Cheney, were natives of New England where their ancestors had settled in colonial times. The family moved from New England to Ohio; Judge Cheney's father was a carpenter and farmer.
Judge Cheney was educated in the schools of Northeastern Ohio. When he completed his education, he engaged in teaching until he took up the study of law in the office of S. A. Northway in Jefferson, Ohio. Subsequently, he went to Toledo and continued law studies with the law firm of Scribner, Hurd, and Scribner, and was admitted to the bar in Ohio in 1877. He practiced there until 1880. Moving west, he became associated with Thomas Wren for a period of a decade, during which time he served as District Attorney of Eureka County and one term in the Nevada Assembly, where he was chairman of the Judiciary Committee. In December 1890, he was appointed District Judge to succeed Judge Bigelow, who had resigned. Judge Cheney was elected to the same office in 1887 and served until 1898.
In 1887, Judge Cheney married Jennie Wethered, of Eureka. They had one son, Everett. In 1902, when Judge Cheney moved to Reno, Cheney formed the firm of Cheney, Downer, Hawkins, and Lundsford. Judge Cheney received the degree of Doctor of Laws in 1908. From 1919 to 1921 he was a regent of the University. He died in Reno on March 13, 1922. A street in Reno is named for Judge Cheney, in the section where his home once stood.