City captain Kompany starts alongside John Stones at the centre of defence while Delph comes in alongside Fernandinho in midfield.
Elsewhere, Raheem Sterling drops to the bench for the visitors and Nolito starts.
For the hosts, Kurt Zouma slots in alongside Gary Cahill and David Luiz, with Cesar Azpilicueta moving to right wing-back.
TEAMS IN FULL:
Read the full article on eurosport.co.uk: Kompany, Delph start for City against Chelsea