Taiwan's Chien, the world's 189th-ranked player, was among the early starters at the Jack Nicklaus designed The Club at Carlton Woods near Houston, mixing six birdies with a bogey to top the leaderboard.
However, she will be looking over her shoulder at a chasing pack of six players including Tokyo Olympic gold medallist Korda, who signed for a 68 along with Japan's Ayaka Furue, Australian Stephanie Kyriacou, South Korea's Chella Choi and Americans Marina Alex and Lilia Vu.
Vu and Kyriacou both jumped up the leaderboard with late eagles, the American's coming on her penultimate hole and the Australian's on her last.
Korda, who is hunting a second major following her triumph at the 2021 Women's PGA Championship, missed last year's Chevron due to injury but is back to full fitness and has four top-six finishes in five starts this season.
"I took advantage of the par-fives today, I think I birdied them all, so that was important," said Korda, who was among the late starters and sat out an hour during a dangerous weather delay. "Overall I played pretty well.
"It was nice to finish the way I did with just a tap-in birdie."
With the Chevron moving to The Club at Carlton Woods after calling the Mission Hills Country Club in Rancho Mirage, California home for 51 years, the nine past champions in the field, including world number one Lydia Ko and 2022 winner Jennifer Kupcho, have no home field advantage.
Kupcho opened her title defence with a level par 72.
Ko had a roller-coaster round including four birdies and three bogeys which left the New Zealander on one-under 71 alongside Canada's twice major winner Brooke Henderson.
"It wasn't my sharpest," said Ko. "But to start off at under par I think is a good way to start this week.
"It's not easy."
Chien certainly found the move to Texas to her liking.
Playing the back nine first, she made the turn at two-under before making her only bogey of the day at the first.
That would be the 32-year-old's only stumble as she recovered in style to card four birdies over her final six holes.
"I saw the pin sheet last night, and I can't sleep," said Chien, who came to the major off her best result of the season, a tie for fourth at last week's LOTTE Championship. "It feels so hard. I think we did very well today."