A positron annihilation study of the icosahedral Al-Cu-Fe alloy system has been carried out using both Doppler broadening and lifetime measurement techniques. Isochronal annealing studies show that a nearly unchanged two-component lifetime spectrum is obtained up to the highest annealing temperature of 450 degrees C used in the present work, indicating the stability of the structure and the defect state in this quasicrystalline phase up to this annealing temperature. The vacancy defect concentration is about 8 ppm which is higher than that observed in the authors' earlier study on icosahedral Al-Mn-Si, though the vacancy size is lower-approximately a monovacancy size on average in Al-Cu-Fe against a divacancy size in Al-Mn-Si. The existence of such a high concentration of vacancy defects even in quasicrystalline Al-Cu-Fe, which has little phason disorder, should be significant from the point of view of developing a structural model for quasicrystals. It appears that a two-component positron lifetime spectrum indicative of a high concentration of vacancy-type defects is characteristic of the icosahedral quasicrystalline phase. The possibility of a central hole in the icosahedral building block in this phase is ruled out from the authors' positron annihilation experiments.