Richard Barrett was born in County Mayo, Ireland in 1838. He eventually moved to the United States and settled in Buffalo, New York. It was there that Barrett enlisted in the United States Army and was assigned to Company A of the 1st U.S. Cavalry Regiment. By 1872, he had risen to the rank of first sergeant. On May 23 of that year, while posted to the Arizona Territory, Barrett volunteered to lead a group of soldiers against a group of renegade Tonto Apaches at Sycamore Canyon. He was cited for "conspicuous gallantry" and recommended for the Medal of Honor for his actions which he received on April 12, 1875. Barrett moved to Washington, D.C. after his retirement from military service. He died there on March 20, 1898, at the age of 60. He was interred at the United States Soldiers' and Airmen's Home National Cemetery.