  We consider the twistor theory approach to Kronheimer's ALE metrics on
resolutions of the quotient of C^2 by a finite subgroup of SU(2). The circle
action on the 4-manifold induces a C^* action on a compactification of the
twistor space and we identify the orbit of a generic twistor line as a nodal
rational curve in a particular cohomology class of a projective rational
surface. Using the results of N.Honda et al we identify this surface with the
minitwistor space for the Einstein-Weyl structure on the 3-dimensional quotient
of the ALE space by the circle action.
