Spain's Rahm, ranked No. 5 in the Official World Golf Ranking, sits on the top of the leaderboard in Hawaii with Collin Morikawa and JJ Spaun.
The three players all shot round of 9-under par 64 at the Plantation Course in Kapalua, a layout that yields plenty of scoring opportunities.
Tom Kim lies just one shot off the pace following a 65, and he produced the shot of the day in the process when holing out for eagle at the par-4 6th.
Asked if he was targeting Smith's score, Rahm stifled a laugh and said:
Rahm is using the new Callaway Paradym driver.
Scheffler was dethroned by Rory McIlroy as the best player in the world late in 2022.
McIlroy has decided not to play this week.
Here's what Scheffler needs to do to regain the top spot.
There are 39 players in the field this week.
It represents the first tournament played on the PGA Tour to have been given "elevated status" with a bumper prize pool of $15m, meaning the winner will take home $2.7m.
The established, American circuit announced that 17 tournaments were to be elevated with bigger prize purses in response to LIV Golf.
American Billy Horschel was the only player in the field to shoot over par on day one, shooting 3-over.
TOURNAMENT OF CHAMPIONS R1 LEADERBOARD
-9 J Rahm, C Morikawa, JJ Spaun
-8 T Kim
-7 M Hughes, T Hoge, A Wise, S Im, S Scheffler, M Fitzpatrick