McDonald birdied all four par-fives at Mission Hills Country Club in Rancho Mirage, California to reach four under.

Thompson, who was left in tears when a four-shot penalty cost her the title in 2017, birdied 17 and 18 to move second.

England's Charley Hull is the best-placed Briton, tied 29th on level par.

Hull's compatriot Jodi Ewart Shadoff dropped shots on the opening four holes but found her touch in an eventful round to finish at one over on a day when only 28 of the 112 players finished under par.

Thompson's putting boost

Thompson won the event in 2014 and looked to have added a second major in 2017 before a dramatic penalty - for marking her ball incorrectly on a green - cost her the title.

In Thursday's opening round, the world number nine struggled off the tee and found the fairway just seven times from 14 drives on a course with ample rough.

"It was a little bit of an up-and-down day," said Thompson, who is one of four players in second on three under.

"I hit some great shots and then hit some poor ones off the tee. I made some great putts, which is always a big confidence booster for me."

Classy Ko keeps it simple

Leader McDonald has never won a major and has just three top-10 finishes on the LPGA Tour.

In contrast, New Zealand's Lydia Ko has finished second, first and third in her past three LPGA starts and again looked in good touch, finding three birdies in a two-under-par round.

"I hit the fairway, so hit the green, two-putt, that's it," said Ko, who won the event in 2016.

South Korea's world number one Park Sung-hyun is one under, while defending champion Pernilla Lindberg of Sweden battled to a 73 to sit one over, a shot better than American Michelle Wie, who was five over early before righting the ship with four straight birdies.

Georgia Hall ended her round with a double-bogey seven on the final hole to finish on two over, while her fellow English players Bronte Law and Charlotte Thomas are six and seven over par respectively.