The battle for Chattanooga was probably more of a turning point. It wasn't a turning point in terms of changing the US odds of winning.
It was more a demonstration of absolute dominance of the US' logistical effort and industrial capacity.
After the battle Thomas' staff reported that from October 20 to December 1, 1863 the US took in 573 deserters and 5,569 prisoners. See Powell, page 180.
Considering that Confederates only reported 361 KIA, and 4,722 WIA, the number of men who quit fighting is astounding. How many men from Kentucky, Tennessee and Mississippi, that had fought for the Confederate cause thought the cause was hopeless and began to rate their duty to their family as more important than their duty to the alleged nation?