Branch was born in Enfield, North Carolina in 1820. He graduated from Princeton in 1838, studied law and served in Congress from 1855 until 1861. Branch commanded a brigade attached to A.P. Hill's Division who made the grueling 17 mile march to the battlefield from Harpers Ferry on the day of the battle. Arriving on the south end of the battlefield, Branch and the other brigades of Hill's division helped turn back Burnside's attack at the end of the day. Like George Anderson, Branch was also buried in Raleigh, North Carolina.