Parry opened with a pair of birdies and closed with another to finish the day one stroke ahead of Simon Khan.
Seven players, including Phil Mickelson, were tied for third at 6-under.
Parry was 4-under through six holes and made the turn at 5-under with a ninth-hole birdie. He added birdies at 14 and 16 before the closing 4 at the par-5 18th gave him the outright lead.
Khan jumped next to Parry among the leaders with an eagle at 18, a 607-yard hole that was playing the easiest on the course Thursday. There were at least nine eagles on the hole in the first round.
Of those tied with Mickelson, only James Morrison played the first round without a bogey.
Mickelson opened his round with a bogey at the 10th hole but eagled the par-5, 599-yard 12th. He had a birdie at 14 and closed his first nine birdie-bogey-birdie. He added front-side birdies at 1, 3 and 6.