The Open Championship: Spieth leads, Woods back in contention
Spieth is on nine under par along with compatriots Xander Schauffele and Kevin Kisner.
Jordan Spieth goes into the final round of the Open as joint leader as he looks to become the first back-to-back winner for a decade.
Along with compatriots Xander Schauffele and Kevin Kisner, the 24-year-old finished day three on nine under par.
But he could find himself in a battle with another former winner - Tiger Woods.
The three-time Open champion rolled back the years in thrilling fashion to revive hopes of a 15th major title and now lurks ominously among the chasing pack after a thrilling day at Carnoustie.
The tone was set when Spieth drove the first green on the 380-yard par four and holed from 12 feet for eagle on his way to a bogey-free 65 to finish nine under par, a total matched by Schauffele and Kisner.
Another American Kevin Chappell is two shots off the lead with Italy's Francesco Molinari on six under and Woods another stroke back alongside Rory McIlroy, Tommy Fleetwood, Webb Simpson, Alex Noren, Matt Kuchar and Zach Johnson.
"I've always wanted to battle it out with Tiger in a major - who hasn't?" Spieth said. "I've played it out at Augusta in my head."
The last player to make a successful title defence was Ireland's Padraig Harrington, who coincidentally won at Carnoustie in 2007 and again 12 months later at Royal Birkdale.
Spieth's victories would be the other way around and make it four wins in his last 15 majors, during which time the 24-year-old has also finished second twice, third and fourth.
One of those runners-up finishes came after blowing a five-shot lead with nine holes to play in defence of his Masters title, while the fourth place came when he finished a shot outside a three-man play-off for the 2015 Open at St Andrews in pursuit of the third leg of an unprecedented calendar grand slam.
"I can certainly draw on the all major championship experiences, good and bad that I've had. I've had a career's worth in a few years," said Spieth, who admitted he found it "difficult" to hand over the Claret Jug when he arrived in Carnoustie on Monday.
"I know as well as anyone that anything can happen in the Open. I'm not getting ahead of myself, I'm just in a good position."
Woods has not played in the Open since 2015 due to injury and is without a victory since 2013, while the last of his 14 major titles to date came a decade ago in the US Open.
But the 42-year-old has made a remarkable return to action since undergoing spinal fusion surgery last April, and a third round of 66 certainly had his legion of fans believing in what had once seemed impossible.
"It seemed like everybody was shooting six, seven under and I figured I could probably do the same and I needed to with the leaders starting at six. I need to go get it," Woods said.
"It's one of my better rounds I've played. I felt I really had control of the ball."
That was certainly not true on the 18th, his tee shot seemingly destined to find the Barry Burn only to take a fortunate bounce to the right to stay on dry land.
But Woods made the most of his good fortune to make par and added: "It kept me in the fight."
England's Justin Rose is a shot behind Woods after earlier equalling the lowest score in an Open at Carnoustie with a brilliant 64.
Rose, who finished fourth in the Open as a 17-year-old amateur 20 years ago, birdied the 18th hole on Friday evening to make the halfway cut with nothing to spare on three over par.
And the Olympic champion carried on where he left off on Saturday, taking advantage of benign conditions to fire seven more birdies to match the 64s recorded by Steve Stricker and Richard Green the last time Carnoustie staged the Open in 2007.
"It was massive to take advantage today," Rose said after the lowest score of his career in any major. "I was very excited last night not to be down the road, ruing another Open opportunity gone. I picked up where I left off and it was a great day's work."