A turbine stator for an aircraft turbine engine is disclosed. The turbine stator includes a stator wall supporting a high pressure air injector fixed on the downstream side, and an annular abradable element support. The lower radial end of the element support is fixed to the high pressure air injector and the upper radial end of the element support is fixed to the stator wall, such that they jointly delimit a cavity under pressure. The turbine stator also includes at least one vibration damping device located in the cavity under pressure. The vibration damping device is in contact with each of the two elements taken among the stator wall and the annular support.