Storm birdied four of his first seven holes and was tied with fellow Englishman Steve Webster at 8-under 136. Five players were a shot back.
Webster had five birdies but finished with a 70 after a double bogey on No. 14 and a bogey on No. 2.
Overnight leader Tano Goya of Argentina shot a 75 after an opening-round 65 to drop to 14th.
Miguel Angel Jimenez of Spain, who helped design the 7,155-yard course at the Prosper Golf resort, shot a second straight 71 and was 2 under.