The last major southern offensive ended the possibility of the south winning the war took place at the battle of

The last major Southern offensive, that ended the possibility of the South winning the war took place at the Battle of  Gettysburg.

Explanation:

One of the most important battles of the Civil War was the Battle of Gettysburg. The battle was fought between July 1 and July 3, 1863, near the town of Gettysburg, Pennsylvania, between the Union army under George Gordon Meade and the Southern army under Robert E. Lee. The victory of the North is considered a turning point in the history of the war.  

Following his victory at the Battle of Chancellorsville in May 1863, Lee led his army went north, hoping to be able to force the North to stop the war. Three days before the battle, President Abraham Lincoln had sacked general Joseph Hoker, and given Meade the command of the Northern army.

The fighting began on July 1, and after fierce fighting around the town of Gettysburg, the North forces were forced to retreat to the hills just south of town. On the second day, Lee attacked the left and right wing of Meade's army, but was defeated by Union troops. On the third day, Lee attacked again. The most important incident was an attack by 12,500 Southern troops known as the Pickett's Charge, against the center of the Union army. Pickett's troops had to retreat with heavy losses, and that led Lee's army back to Virginia.

The battle of Gettysburg saw the heaviest casualties of the Civil War, with between 46,000 and 51,000 killed or wounded. In November, a cemetery was dedicated in Gettysburg to re-bury the dead from the battle, and it was on this occasion that Abraham Lincoln gave the Gettysburg Address.