Alexander H. Mitchell (November 13, 1840–March 7, 1913) was a United States military officer who fought with the Union Army during the American Civil War as captain of Company A of the 105th Pennsylvania Infantry. Wounded multiple times in combat during the war, he was awarded the Kearny Cross for his distinguished service in the Battle of Chancellorsville, Virginia in May 1863, and was then also awarded his nation’s highest award for valor, the U.S. Medal of Honor for his capture of a Confederate flag in hand-to-hand combat with the color-bearer of the 18th North Carolina Infantry during the Battle of Spotsylvania Court House on May 12, 1864.