  We construct new supersymmetric black ring solutions on the Eguchi-Hanson
base space as solutions of five-dimensional minimal supergravity. The solutions
have the same two angular momentum components and the asymptotic structure on
timeslices is asymptotically locally Euclidean. The S^1-direction of the black
ring is along the equator on a S^2-bolt on the Eguchi-Hanson space. We also
investigate the limit to a black hole, which describes the BMPV black hole with
the topology of the lens space L(2;1)=S^3/Z_2.
