  Quantum non-perturbative geometry of the universal hypermultiplet is
investigated. We consider the simple case when the D-instantons, originating
from the Calabi-Yau wrapped D2-branes, preserve a U(1)xU(1) symmetry of the
universal hypermultiplet moduli space. The cluster decomposition of
D-instantons is proved to be valid in a curved spacetime. We find an SL(2,Z)
duality-invariant quaternionic solution to the effective NLSM metric of the
universal hypermultiplet, which is governed by a modular-invariant function.
This function appears to be the same function found by Green and Gutperle, and
describing the modular invariant completion of the R^4 term by the D-instanton
effects in the type-II superstring/M-theory. We argue that our solution
interpolates between the perturbative (large CY volume) region and the
superconformal (Landau-Ginzburg) region in the universal hypermultiplet moduli
space. We also calculate a non-perturbative scalar potential in the
hyper-K\"ahler limit, when an abelian isometry of the universal hypermultiplet
moduli space is gauged in the presence of D-instantons.
