  We determine the instanton corrected hypermultiplet moduli space in type IIB
compactifications near a Calabi-Yau conifold point where the size of a
two-cycle shrinks to zero. We show that D1-instantons resolve the conifold
singularity caused by worldsheet instantons. Furthermore, by resumming the
instanton series, we reproduce exactly the results obtained by Ooguri and Vafa
on the type IIA side, where membrane instantons correct the hypermultiplet
moduli space. Our calculations therefore establish that mirror symmetry holds
non-perturbatively in the string coupling.
