The Englishman made a solid start at Muirfield Village on Thursday as he looks for a first PGA title with six of his eight birdies coming in 10 holes as he notched up a seven-under-par tally.
Rose is joined at the top of the leaderboard by American Rickie Fowler and Australian Geoff Ogilvy.
Rose, who has previously clinched two top-five finishes at the Memorial Tournament, including runner-up to American Kenny Perry two years ago, said: "I feel like I've been comfortable with my game for a number of weeks, and I'm not really trying to do anything different.
"This is a tournament that I feel like I should have won, for sure.
"I always feel comfortable when I do get here. I like all the tee shots, and the greens are so pure here that if you do get a putting stroke going, you're going to make some putts."
Phil Mickelson, who could knock Tiger Woods off the world number one spot for the first time in 260 weeks, is two shots off the leaders, while defending champion Woods struggled to a 72.
If Mickelson wins and Woods finishes outside of the top four he will take over as number one.