Webb Simpson and Gary Woodland were tied for the clubhouse lead at nine under but Kuchar was one shot better off as he made it to the 13th on five under for the round before play was suspended in fading light.
"I've been playing some good golf," Kuchar on the PGA website after a bogey-free round so far.
Woodland birdied on four of the last five holes propelling him to a 64 and a share of the lead alongside Simpson, who carded a 66 and acknowledged he needed to enjoy his lead while it lasted.
"A lot of guys are playing good golf and my guess is at the end of two rounds I won't be leading because there are a lot of birdie holes," he said.
Rickie Fowler and Keegan Bradley were two shots further back after rounds of 64 and 63 respectively, with Justin Rose almost among those at seven under after reaching the 14th at four under par.
Overnight leader Kevin Stadler was struggling as he made it through 13 holes before play was suspended. Attacking the back nine first, he suffered a double bogey on the 17th as he was two over par and in a tie for 15th place.
Tiger Woods cancelled out three early birdies with three bogeys to sit in that same huddle on five under par.
The world number one had complained of neck and back pains through his round.
"I'm a little sore right now, yeah," Woods said.
"I got off to a great start today [Friday] and then lost it the middle part of the round and made too many mistakes. Didn't hit any greens. Consequently, made some bogeys."