We show that the explicit ALE Ricci-flat Kahler metrics constructed by Eguchi-Hanson, Gibbons-Hawking, Hitchin and Kronheimer, and their free quotients are Tian-Yau metrics. The proof relies on a construction of appropriate compactifications of Q-Gorenstein smoothings of quotient singularities as log del Pezzo surfaces. Time permitting, a geometric description of the compactifications will be provided. This is a joint work with I. Suvaina.