This is the only five-round tournament on the PGA TOUR schedule. The format sees each player grouped with amateurs over the first four rounds before the cut is made.
Allenby fired his 63 at LaQuinta.
Reigning Masters champion Phil Mickelson made his 2007 debut on Wednesday at La Quinta and turned around what could have been a disastrous round. He dropped three shots in his first four holes, but rebounded with a 2-under-par 70.
Mickelson, who has not played competitively since the Ryder Cup in September, is tied for 47th place.
He was 1 over par on his front nine thanks to two bogeys, a double-bogey and three birdies, but flew out of the gate on the second nine.
He holed a 4-foot birdie putt at the 10th and collected back-to-back birdies at the par-5 11th. Mickelson drained a 20-footer for his third consecutive birdie at 12. At the par-5 13th, Mickelson missed the green, but his vaunted short game bailed him out with a tap-in birdie.
Mickelson dropped a shot at the 14th when he came up short of the green with his second. That storied short game let him down as his chip came up 20 feet short and the three-time major champion missed the par putt. Mickelson parred out for his 70.
Mark Calcavecchia and Craig Kanada are tied for second place after both opened with rounds of 7-under-par 65. Calcavecchia shot his 65 at The Classic Course, while Kanada posted his score at Bermuda Dunes.
Allenby began his round on the back nine and collected his first two birdies at his first two par-5s, the 11th and 13th. He added birdies at 14 and 16 to make the turn at 4-under-par 32.
On his second nine, Allenby flew out quickly with a birdie at one. He tallied back-to-back birdies at five and six to move into sole possession of the lead at minus-7.
Allenby ran into trouble at the par-3 seventh, but holed a 6-foot par save. At his final two holes, Allenby sank a pair of 25-footers for birdie to shoot his lowest number at this tournament.
Allenby had an interesting round due to the fact that the scorekeeper following him gave him credit for eagles on two holes, when in fact, he made birdies. For a period of time, it looked like Allenby would flirt with a magical 59, but he knew his correct score all along.
'The scorekeeper was trying to be nice to me, but I don't think he was all there today,' joked Allenby. 'Every time I made a birdie, he came up trying to shake my hand. Not quite sure what the situation was there. And then obviously the Golf Channel thought I was trying to shoot 59 or 60, probably like everyone else. But I knew what was going on.
'But I played well, tee-to-green I played really well and I made a lot of putts obviously. I made all the short ones and made a lot of putts from 10 feet.'
Charley Hoffman. Dudley Hart, Scott Verplank, Matt Kuchar, Jason Gore, Tripp Isenhour, Bob Heintz and Johnson Wagner are knotted in fourth place at 6-under-par 66.
Former world No. 1 David Duval got off to a strong start on Wednesday. He recorded three birdies and an eagle for a 5-under-par 67 at The Classic Course and is part of a group tied for 12th place.
'I feel like I'm playing well,' said Duval, who shot a 59 at the Palmer Course en route to victory in 1999. 'I finished up last year, I think, for the most part accomplishing my major goals.'
Last week's surprising Sony Open in Hawaii winner Paul Goydos carded a 4- under-par 68, while defending champion Chad Campbell joined Mickelson at minus-2.