With one more win, Roma can match Tottenham's 11 straight victories in 1960-61 for the best start in a major European league.
The Giallorossi's next match comes at Torino on Sunday.
Roma had already broken the Serie A record for best start, previously held by Juventus.
Juventus recorded eight opening victories in 1930-31 and 1985-86, and also won nine straight matches to start 2005-06 but was stripped of its title-winning season in the "calciopoli" match-fixing scandal.
Perhaps even more impressive than the winning streak is Roma's scoreline thus far, with 24 goals scored and only one conceded.
"(Chievo) doesn't deserve to be last. They played really well, as a squad," Roma coach Rudi Garcia said. "I had said it would be a difficult match and I wasn't wrong. We're missing some key players in attack but the important thing was to win, make it 10 out of 10."
Roma remained without captain Francesco Totti and key forward Gervinho, who are each injured and out for several weeks. Also, fullback Maicon was suspended.
Roma's last loss in Serie A came against Chievo at the Stadio Olimpico in May.
For a while, it looked like Chievo might again come away with at least a point.
While Roma dominated the first half, Chievo often defended with eight or nine men and the Giallorossi had trouble getting shots on goal.
Marquinho and Kevin Strootman threatened for Roma with long-range efforts early on and Miralem Pjanic couldn't get his free kicks around or over Chievo's wall.
Unable to create much of anything at the start of the second half, Roma's first-year coach Rudi Garcia sent on Florenzi for Marquinho and the match soon turned.
Borriello had a chance to score again in the 81st but his shot was blocked, and Adem Ljajic put a dangerous, angled free kick on goal two minutes later but Chievo goalkeeper Christian Puggioni did well to push the shot over the bar.
Chievo remained rock bottom, two points behind Catania and promoted Sassuolo.
It was Chievo's sixth consecutive loss, and the defeat could cost coach Giuseppe Sannino his job.