On June 3, 1864, General Robert E. Lee effectively won his last victory of the Civil War at the Battle of Cold Harbor. From the article:
"Lee’s Confederate veterans to abandon much of northern Virginia. The small crossroads of Cold Harbor, just 10 miles north of Richmond, became the focal point of the action in late May. From May 31–June 3, Ulysses S. Grant ordered repeated attacks against entrenched Confederate positions, culminating in an enormously bloody repulse on June 3. Both armies held their ground and kept up a withering fire between the lines until June 12, at which point Grant withdrew but continued to move east and south. The Army of the Potomac crossed the James River and, by June 16, was in position to directly threaten the manufacturing and rail center of Petersburg—a critical gateway to Richmond."