Cheyenne, who turns 23 next week, sank four birdies on the front nine and four more on the back, with a bogey on the 15th hole the only blemish, to lead a Ladies European Tour event for the first time in her career.
"I had birdies here and there and my putting was great," Cheyenne, the daughter of Tiger's half brother Earl Junior, said on the Tour website (www.ladieseuropeantour.com).
"I just played really steady. Everything clicked today so I felt great. Hopefully I can continue just part of that tomorrow," she said, adding that she would try to watch Tiger's opening round at the British Open.
"At 2.45 I think somebody is teeing off ... so I'll try and catch that. But I'll hit a few balls and practice a little, get some lunch and just rest."
Tiger, chasing an 18th major triumph, made a poor start at Muirfield, bogeying the first hole after a hooked drive into the rough.
The world number one then returned to level par with a birdie at the fourth before another bogey at the sixth left him at one over after nine holes.
(Reporting by Iain Rogers, editing by Alison Wildey)
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