  Toric Ricci--flat metrics in dimension four correspond to certain holomorphic
vector bundles over a twistor space. We construct these bundles explicitly, by
exhibiting and characterising their patching matrices, for the five--parameter
family of Riemannian ALF metrics constructed by Chen and Teo. The Chen--Teo
family contains a two--parameter family of asymptotically flat gravitational
instantons. The patching matrices for these instantons take a simple rational
form.
