If Griffiths wins Burghley, he will need to triumph at Kentucky next April to capture the £215,000 Rolex Grand Slam of Eventing.
It is awarded to any rider who completes consecutive Badminton, Burghley and Kentucky victories, but has only been achieved once before - by Britain’s Pippa Funnell - 11 years ago.
“The dream is still on,” said Griffiths, whose score of 40.2 penalties gave him a narrow advantage over his fellow Australian Andrew Hoy, who first won Burghley 35 years ago, with American Allison Springer lying third.
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“I knew he could go in and do a beautiful test, and he came up with the goods.
“The cross-country course on Saturday is a traditional, massive Burghley. You need a really special horse to jump around this course, and I’ve got a horse that I know can do it.”
Oxfordshire-based Izzy Taylor, meanwhile, produced a solid test aboard KBIS Briarlands Matilda to score 48.3 and stand sixth as she continued putting World Equestrian Games disappointment behind her.
Taylor was an original World Games selection for the Great Britain team with Allercombe Ellie, only for the horse to suffer an injury during squad training, then one of her other contenders Orlando did not get a call-up off the reserve list, either to replace Allercombe Ellie or Pippa Funnell’s Billy Beware, who also went down injured.
“It was tough,” Taylor said.
“To have Ellie selected and then for it to go wrong is never nice, then to be sitting and waiting with Orlando, it was like a double blow in some ways.
“Last week wasn’t the best of weeks. It is always difficult when there is a big event on and you are not there when you feel you could, or should, have been.
“I felt with the two of the horses I had a double chance, so it was quite hard.”
Jonathan Paget, who won the title last year before being stripped of the crown, is one of the early day two starters when the event will crank up a notch.
Other riders in the dressage arena on Friday include Britain’s world number one William Fox-Pitt, recently returned from winning individual bronze and team silver at the Alltech FEI World Equestrian Games in Normandy last weekend, the 2009 Burghley champion Oliver Townend, plus hat-trick hopeful Andrew Nicholson.
Day One Standings - Dressage
1: HAPPY TIMES - Sam Griffiths - 40.2
2: RUTHERGLEN - Andrew Hoy - 40.8
3: ARTHUR - Allison Springer - 41.2
4: WESTWOOD MARINER - Piggy French - 45.8
5: RF DEMETER - Marilyn Little - 47.5
6: KBIS BRIARLANDS MATILDA - Izzy Taylor - 48.3
7: VALENTINO V - Sarah Bullimore - 49.5
8: REHY TOO - Gina Ruck - 50.5
9: GLENGARNOCK - Paul Sims - 51.3
10: FINBURY HILL - Hannah Bate - 51.5