Claxton and Kirkpatrick each shot 7-under-par 65s at the Dakota Dunes Country Club to lead Tjaart van der Walt and Chris Couch by a shot.
Claxton is in search of his second victory of the year, as is Couch. Couch won the season-opening Florida Classic, while Claxton claimed the Louisiana Open two weeks later.
Claxton, in his sixth season on the developmental tour, played his first seven holes in 6-under-par Thursday. He then recorded one birdie and ten pars over his final 11 holes.
Kirkpatrick, a 31-year-old Englishman who attended the University of Alabama, has missed three of his last four cuts. Starting at the 10th, Kirkpatrick was 1-under through eight holes. He went on to birdie the 18th, 1st, 3rd and 4th holes. He finished his scoring with an eagle-3 on the par-5 7th.
Full-field scores from the Buy.Com Siouxland Open