Gallagher, who has been handed the captain's armband on numerous occasions this campaign, has missed just one Premier League fixture this season, a result of a ban.
However, the England international is only selected among the replacements as Mauricio Pochettino names an attack-minded starting lineup with Chelsea 1-0 down on aggregate.
Just two changes have been made from the team that started the 1-0 victory over Fulham on January 13, Malo Gusto also missing out but through muscle overload.
Ben Chilwell makes his first start since recovering from a hamstring injury, while Mykhaylo Mudryk is handed an opportunity in the final third.
Armando Broja also starts despite speculation regarding his future, with Carney Chukwuemeka and Noni Madueke being named among the replacements.
Meanwhile, Michael Carrick has made four alterations to the Middlesbrough XI that started the 1-1 draw with Rotherham United at the weekend.
Luke Ayling, Isaiah Jones, Finn Azaz and Sam Greenwood are the quartet to miss out, all but Jones not featuring due to being cup-tied.
Rav van den Berg comes back into the team at right-back, while Jonny Howson, Matt Crooks and Marcus Forss are selected further forward.
Chelsea: Petrovic; Disasi, Silva, Colwill, Chilwell; Caicedo, Fernandez, Palmer; Mudryk, Broja, Sterling
Subs: Bergstrom, Curd, Badiashile, Gilchrist, Gallagher, Chukwuemeka, Castledine, Madueke, Washington
Middlesbrough: Glover; Van den Berg, Clarke, Fry, Engel; Hackney, Barlaser, Howson; Rogers, Crooks; Forss
Subs: J.Jones, Gilbert, Dijksteel, McNair, Coburn, O'Brien, McCabe, Bridge, Bilongo