  We use the twistorial construction of D-instantons in Calabi-Yau
compactifications of type II string theory to compute an explicit expression
for the metric on the hypermultiplet moduli space affected by these
non-perturbative corrections. In this way we obtain an exact quaternion-Kahler
metric which is a non-trivial deformation of the local c-map. In the
four-dimensional case corresponding to the universal hypermultiplet, our metric
fits the Tod ansatz and provides an exact solution of the continuous Toda
equation. We also analyze the fate of the curvature singularity of the
perturbative metric by deriving an S-duality invariant equation which
determines the singularity hypersurface after inclusion of the D(-1)-instanton
effects.
