Chawrasia had three birdies against one bogey, while Jeev struck an eagle, a birdie and two bogeys, one of them on his first hole.
Danny Willett, in his first appearance on home soil since his victory at Augusta National, lived up to his top billing with a sparkling six-under 66 in the first round.
The 28-year-old Englishman, the highest ranked player in the field, was the only player not to drop a shot at Wentworth Club and sits one stroke behind the trio of Australian Scott Hend, Dutchman Joost Luiten and Korean YE Yang.