Fox-Pitt currently sits third in the overall standings with Parklane Hawk following the completion of the cross country phase, an improvement of two places from his ranking after the dressage.
The 44-year-old, who claimed his third Olympic medal with team eventing silver at London 2012, went clear with Parklane Hawk on the cross country phase, one second inside the optimum time.
Double Olympic champion Michael Jung leads the way with New Zealand's Jonathan Paget second but the latter and Fox-Pitt are within a fence of the overnight leader with the showjumping to come.
Officials have determined that a win for Fox-Pitt would constitute the Grand Slam, awarded if a rider claims successive victories at Kentucky, Badminton and Burghley.
He won Burghley in 2011 and Kentucky last year before bad weather forced the cancellation of Badminton 12 months ago, denying him the Grand Slam.
Fox-Pitt has a very realistic chance of becoming only the second rider to achieve the honour although he knows the performances of his rivals could either make or break it.
Fox-Pitt had a run-out on his first ride Oslo during the cross country and he said: "Oslo and Parklane Hawk are very different but they both gave me great rides.
"Naturally I was very disappointed about my 20pen on Oslo, I didn't steer him properly, but on Parklane Hawk I managed to keep hold of my reins.
"We've got a long way to go, starting with the trot-up. I'm not going into the showjumping in the lead, so I've got to rely on the two guys above me making mistakes and I've got to go clear."