Cheetham finds form to cut Brier's lead
Cheetham fired a first round 67 at Oitavos Golf Club as the late starters took advantage of calmer conditions on Portugal's Atlantic coast.
The 37-year-old holed from 6ft on the seventh, 12ft on the next and 8ft on the 13th.
A bogey on the 18th left him on four under, two behind leader Brier, who defied the wind to card a 65.
"I can't remember ever having three eagles in a round before," said Cheetham.
"That was incredible and a real bonus because it was difficult in that wind, it was really swirling around."
Earlier in the day one costly lapse in concentration sent pre-tournament favourite Nick Dougherty tumbling off the leaderboard.
Dougherty had just carded his second birdie in a row to lie one shot off the lead when he fell foul of the daunting 18th.
The 22-year-old drove out of bounds on the 474-yard par four and then hit his second ball into a bush to the left of the fairway.
After taking a penalty drop, the Englishman missed the green with his approach and needed three more shots to get down from the edge of the green, running up a quadruple bogey eight. From two under par Dougherty slumped to two over and after another bogey on the fifth, needed to birdie his last two holes to record a one over par 72.
"It's disappointing but I played quite nicely apart from that one hole," said Dougherty, who held off Ryder Cup stars Colin Montgomerie and Thomas Bjorn to win his first tour title in Singapore in January.
"I knew my drive would be in the trees but once we got up there the out of bounds fence was very close to the tree line and one of the TV guys said it had gone out.
"It makes it so much more difficult when the wind blows and it was good to shoot one over. My attitude was very good and I was very calm and relaxed.
"There's three rounds to go, I'm not in bad shape and I'm obviously playing good enough golf.
"As long as I don't make mistakes like that any more I think I will be there or thereabouts," said Dougherty.
Dougherty was one of the early starters who faced the toughest conditions, with only 11 out of 78 players breaking par.
Among them was France's Jean Van de Velde, who carded an encouraging one under par 70 on his fourth comeback from a serious knee injury.
Van de Velde has undergone two bouts of reconstructive surgery and made three attempts to return to the European Tour on a medical exemption last season, only to miss the cut in eight of his 14 tournaments and was in too much pain to attempt to earn his card at the qualifying school.
As a result the popular Frenchman has to rely on invites to compete on tour, a situation which would have been avoided if he had taken anything less than a triple-bogey seven on the final hole of the Open championship in 1999.
Victory at Carnoustie, which eventually went to Paul Lawrie in a play-off, would have given Van de Velde a 10-year exemption.
"I'm very happy," said Van de Velde, who recovered from a double bogey on the treacherous 18th to fire five birdies.
"Some of it was extremely good, some not so good but overall I'm pleased.
"It was a difficult day but I tried to keep as cool as I could.
I can't believe how tired I am but the knee was perfect, I think it was more due to the emotion of playing competitive golf again.
"The heart was beating a little quicker on the first tee so that was a good sign I thought."
Gary Murphy is the best of the Irish after carding a two under par 69, while Damien McGrane lies a stroke further back. A double bogey on the 17th saw Peter Lawrie slip to one over, with Philip Walton three shots back. Despite being among the late starters, Stephen Browne ended up on 10 over and a certainty to miss the cut.
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