A turbine engine annular combustion chamber, including longitudinal walls connected by a transverse chamber bottom and a single-piece cowling, the chamber bottom and the cowling each including an inner flange and an outer flange each with a plurality of holes made in it for the passage of fixing systems for fixing the cowling on the chamber bottom. Each fixing system has associated with it at least one tangential slot formed on the corresponding flange of the chamber bottom and/or on the corresponding flange of the cowling, each slot being formed in the immediate vicinity of the corresponding fixing system.