Steven Jeppesen and Gregory Bourdy are also at 4-under par, but only completed 13 holes of the opening round, which was suspended due to darkness on Thursday.
After one hour of the first round, with the first group completing only four holes, heavy rain hammered the Centro National de Golf. There were several attempts to return to the course, but play finally resumed almost eight hours later.
It was not until 10:40 a.m. (ET) that the golfers were back in position. Some of the first half of the draw completed round one, but no one in the second half even teed off.
The plan is to try and catch up over the next two days.
Stephen Gallacher and Terry Pilkadaris are knotted in fourth place at minus- 3. Both are deep into the back nine of their first rounds.
Begay began on the back nine Thursday and the round did not start well. He tallied one bogey and five pars through his first six holes, but went on a mini-run from there.
He recorded back-to-back birdies at 16 and 17, but dropped a shot at the closing hole to make the turn at even-par 36.
On the second nine, Begay, a former college teammate of Tiger Woods at Stanford University, caught fire. He birdied every other hole from the first to the seventh to move into a share of the lead.
'It was a tremendously gratifying round of golf,' said Begay. 'I didn't expect a whole lot so I went out there and tried to defend myself as best as possible.'
Begay, who is playing the European Tour after losing his card on the PGA TOUR last year, has battled various elements all week before the rain ever entered the picture.
His luggage did not arrive until Tuesday and Begay was unable to play one practice round, stepping on the course for the first time for Thursday's opening round.
Begay has battled a back injury for the last few years and the problem resurfaced a bit this week.
'My back's been bugging me a little bit this week,' said Begay. 'I had never seen the course and sometimes you do a little bit better.'
Former Ryder Cuppers Miguel Angel Jimenez and Paul McGinley are tied in the clubhouse with Carlos Rodiles at 2-under-par 70. Amateur Gonzalo Berlin, Carlos Balmaseda, Carlos Del Moral and Jonathan Lomas are two-under par through 12 holes.
Darren Clarke struggled late on Thursday and finished with a 3-over-par 75.
Defending champion Niclas Fasth was one of the many who did not tee off on Thursday.