Parkhomenko was born to a peasant family on 24 December 1893 in the village of Yekaterinovka, Stavropol Governorate. He graduated from primary school and was drafted into the Imperial Russian Army in September 1914 during World War I. Parkhomenko was sent to the Caucasus front, where he served with the 13th Turkestan Rifle Regiment of the 4th Turkestan Rifle Division, initially as a "ryadovoy". There he graduated from the regimental training detachment in 1915 and served as a "yefreytor", junior and senior "unter-ofitser", and "feldfebel". In June 1916 Parkhomenko graduated from a warrant officers school and became a "podpraporshchik". After the Russian Revolution, he was demobilized in December 1917 with the rank of "praporshchik".