An annular combustion chamber has an inner wall and an outer wall of ceramic matrix composite material, together with a chamber end wall that is connected to the inner and outer walls. Elastically-deformable link elements connect the inner wall and the outer chamber walls to inner and outer metal casings. Each of the inner and outer chamber walls is subdivided circumferentially into adjacent sectors along longitudinal edges, each sector extending continuously from the end wall to the opposite end of the chamber and being folded outwards from the chamber at each of its longitudinal edges to form a portion having a U-shaped cross-section terminated by a folded-back margin that is spaced apart from the outer face of the corresponding chamber wall. The link elements are connected to the inner and outer chamber walls by being fastened to the sector margins.