The Teessider, whose only European Tour win came at the 2007 French Open, had seven birdies in a bogey-free 63 to take a two-shot lead.
Martin Kaymer, Fabrizio Zanotti of Paraguay and Raphaël Jacquelin of France are tied for second.
Kaymer, the German 2010 US PGA champion and former world number one, had an eagle at the 12th in his round.
Ryder Cup team-mate Peter Hanson is among a group of six players, a shot further back, on four-under.
Three-time winner Paul Casey, who has missed his last seven cuts, finished on three under-par.
Storm is 114th in the Race to Dubai and faces a battle to retain his European Tour card but was happy with his return to form.
"You can get punished round here but I played the best I have probably played all year. I'm just happy to get a round like that under my belt after recent months," he said.
I made the birdies when I gave myself the chances and got up and down when I missed the greens.
“The golf course here is fantastic - the best I have ever seen it - so you have to hit it straight and that is what I did.
“There is still a lot of play for this season. Keeping my card is the goal. At the start of the season it was getting into the top 60 on The Race to Dubai but I'm a long way from that so my goal now is to keep my card.”