Simon Keogh, Ronan McCormack and Devin Toner have been included amongst the replacements.
Looking forward to the game, former Ireland Under-20 centre O'Malley said: "At this stage of the season we're all dying to play games.
"Having missed out on a fair bit of rugby over the last year through injury, I now feel fit and fresh and it was good to get a game under my belt against Ulster last week. Even though we lost that game, there were positives and we're keen to build on them this week.
"Obviously selection for the Magners League game next week against the Scarlets is a carrot for the players, but we're not looking past this week because we have a lot of respect for Exeter and we have done a lot of video work on them.
"They're going strong and they're a club with big ambitions to become a force in the Guinness Premiership.
"They're pushing for promotion and it will be a tough game for us but the experience of winning on the road in Plymouth back in November will stand to us and training this week has been sharp.
"The British & Irish Cup has given each of us a further incentive to impress and with big games coming up in the Magners League, we all see this week's game as a chance to impress as well as keep up our winning form."
Meanwhile, Exeter have two former Leinster players in their starting line-up, in the form of prop Ruaidhrí Murphy and lock David Gannon.
LEINSTER (v Exeter Chiefs): Girvan Dempsey; Niall Morris, Eoin O'Malley, Shaun Berne, David Kearney; Ian Madigan, Paul O'Donohoe (capt); Stan Wright, Richardt Strauss, Mike Ross, Trevor Hogan, Malcolm O'Kelly, Eoin Sheriff, Paul Ryan, Stephen Keogh.
Replacements: Jason Harris-Wright, Ronan McCormack, Devin Toner, Ciaran Ruddock, David Moore, Kyle Tonetti, Simon Keogh