Kite fired an 8-under 64 in the second round, shooting a 29 on the back nine to reach 10-under-par 134 for the tournament. That's one stroke better than Andy Bean, who shot a 65 to get to 9 under.
Mitch Adcock -- who held the overnight lead for the first time ever on the Champions Tour -- is in third place at minus-7 after a second-round 70. He is two shots better than Tom Purtzer (70).
Kite's front nine was unspectacular -- one bogey at the par-4 fifth -- until the ninth, where he knocked a fairway wood within 6 feet to set up an eagle three.
That got him rolling, and the seven-time Champions Tour reeled off four straight birdies after that to reach minus-7.
'It was one of those days where not much was happening early,' said Kite. '[But] the eagle at the ninth got me going.'
Kite's birdie putts on holes 10-13 ranged from 5 to 15 feet. Two were set up by his eight iron, and two by his 9-iron.
'I have lots of confidence on this course,' Kite said of Valencia Country Club. 'It's one of the best driving courses we play on the Champions Tour. Just enough rough to give you some problems.'
On Sunday, there won't be many players who can give Kite problems.
In the 78-player field, only 22 are under par through two rounds. Bean, Adcock and Purtzer -- being within five strokes -- are the only real challengers.
Still, Kite is less than comfortable.
'I've got to play well tomorrow,' he said. 'Lots of guys can have the type of round I had today. I don't have many 29s.'
Kite will be looking for his first Champions Tour win since the 2004 3M Championship.
After Purtzer, three players share fifth place at minus-4, including Loren Roberts, who is already a three-time winner this season, and defending champion Des Smyth. Ben Crenshaw is the other.