Jonelle Price is the best-placed of the New Zealand eventers, after the dressage phase of the Burghley Horse Trials on Saturday (NZ time).
She's recorded a score of 28.4 penalty points on Faerie Dianimo to sit seventh equal.
Husband Tim Price - the defending champion - is ninth equal on Ringwood Sky Boy, with a score of 28.7.
Tim Price is also 11th equal on Bango and 20th on Xavier Faer.
"Burghley is just the 'Holy Grail' as everyone always says," says Tim. "We just want to come and do a really good job at such a tough track as this.
"Now, it is a bit different for me having won it - it brings a different stigma, but I am just trying to ignore that and just get on with my job, and take every little mini step as it comes along."
British riders dominate the leaderboard, with Pippa Funnell and MGH Grafton Street leading on 22.8, Oliver Townend and Ballaghmor Class in second on 25.3 and Izzy Taylor on Springpower in third on 25.6.
Other Kiwis in the field are Dan Jocelyn aboard Blackthorn Cruise, who are in 25th on 32.3, Caroline Powell aboard On the Brash is in a tie for 43rd on 37.1 and Burghley debutant Samantha Lissington on 39.1 with Ricker Ridge Rui.
The riders will next contest the cross-country phase, which starts on Saturday night.