The 44-year-old, who has won the Kentucky title twice in the past three years, is in fourth place after 23 of the 46-horse field performed their dressage tests.
Fox-Pitt scored 46.2 aboard Seacookie, with whom he finished as runner-up at the Burghley Horse Trials in 2010, with his test with Chilli Morning still to come.
New Zealand's Andrew Nicholson leads the way after scoring 40.8 on Calico Joe before home hope Becky Holder and Can't Fire Me in second with 44.2.
Shandiss McDonald of Canada is third with Rockfield Grant Juan having scored 45.7 while Fox-Pitt's British teammate James Alliston was 21st with Parker.
He will return with Jumbo's Jake and Tivoli as the second half of the field competes including Fox-Pitt's Olympic silver-medal winning teammate from London 2012 Mary King.
King, who claimed the Kentucky crown in between Fox-Pitt's victories in 2011, is riding just Fernhill Urco as she bids to get back to winning ways in Lexington.