Kemper was born in Mountain Prospect, Madison County, Virginia, the son of William and Maria E. Allison Kemper and brother of Frederick T. Kemper (the founder of Kemper Military School). His grandfather had served on the staff of George Washington during the American Revolutionary War, but he himself had virtually no military training. He graduated from Washington College (now Washington and Lee College) in 1842, becoming a lawyer.

After the start of the Mexican-American War, he enlisted and became a captain and assistant quartermaster in the 1st Virginia Infantry, but he joined the service too late (1847) to see any combat action. By 1858 he was a brigadier general in the Virginia Militia.

Kemper was elected to the Virginia House of Delegates in 1853. He became chairman of the Military Affairs Committee, where he was a strong advocate of state military preparedness. In early 1861 he became Speaker, a position he held until January 1863. Much of his term as Speaker coincided with his service in the Confederate States Army.

After the start of the Civil War, Kemper served as a brigadier general in the Provisional Army of Virginia, and then a colonel in the Confederate States Army, commanding the 7th Virginia Infantry starting in May 1862. His regiment was assigned to Brig. Gen. A.P. Hill's brigade in Maj. Gen. James Longstreet's division of the Confederate Army of the Potomac from June 1861 to March 1862. He saw his first action at the First Battle of Bull Run. After a gallant performance at the Battle of Seven Pines during the Peninsula Campaign, Kemper was promoted to brigadier general on June 3, 1862, and briefly commanded a division in Longstreet's Corps. Upon the return to duty of wounded Maj. Gen. George E. Pickett, Kemper reverted to brigade command, the highest role in which he would serve in combat.

At the Second Battle of Bull Run, Kemper's brigade took part in Longstreet's surprise attack against the Union left flank, almost destroying Maj. Gen. John Pope's Army of Virginia. At the Battle of Antietam he was south of the town of Sharpsburg, defending against Maj. Gen. Ambrose E. Burnside's assault in the afternoon of September 17, 1862. He withdrew his brigade in the face of the Union advance, exposing the Confederate right flank, and the line was saved only by the hasty arrival of A.P. Hill's division from Harpers Ferry.

At the Battle of Fredericksburg, Kemper's brigade was held in reserve. In 1863, the brigade was assigned to Pickett's Division in Longstreet's Corps, which meant that he was absent from the Battle of Chancellorsville, while the corps was assigned to Suffolk, Virginia. However, the corps returned to the army in time for the Gettysburg Campaign.

At the Battle of Gettysburg, Kemper arrived with Pickett's Division late on the second day of battle, July 2, 1863. His brigade was one of the main assault units in Pickett's Charge, advancing on the right flank of Pickett's line. After crossing the Emmitsburg Road, his brigade was hit by flanking fire from two Vermont regiments, driving it to the left and disrupting the cohesion of the assault. Kemper rose on his stirrups to urge his men forward, shouting "There are the guns, boys, go for them!"

This bravado made him a more visible target and he was wounded by a bullet in the abdomen and thigh and captured by Union troops. He was rescued by Sgt. Leigh Blanton of the 1st Virginia[1] and was carried back to Confederate lines on Seminary Ridge. General Robert E. Lee encountered Kemper being carried on a stretcher and inquired about the seriousness of his wound, which Kemper said he thought was mortal. He requested that Lee "do full justice to this division for its work today."[2] During the Confederate Army's retreat from Gettysburg, Kemper was again captured by Union forces. He was exchanged (for Charles K. Graham) on September 19, 1863.[3] For the rest of the war he was too ill for combat, and commanded the Reserve Forces of Virginia. He was promoted to major general on September 19, 1864.

It had not been possible to remove the bullet that had wounded Kemper at Gettysburg, and he suffered from groin pain for the rest of his life. After the war he worked as a lawyer and served as the first Governor of Virginia after Reconstruction from January 1, 1874, to January 1, 1878. Jones (1972) argues that Kemper and like-minded Conservatives implemented r acial policies which were less anti-Negro and which gave fuller recognition than historians have conceded. The Virginia Redeemers attempted to shape race relations to conform to what C. Vann Woodward has defined as the Conservative philosophy. Jones concludes that Kemper and the Virginia Redeemers deserve to rank in history alongside the Wade Hamptons and other proponents of the Conservative philosophy.[4]

He died in Walnut Hills, Orange County, Virginia, where he is buried.