Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds is an outstanding open problem. We address this issue by writing the quaternionic geometry on the hypermultiplet moduli space in terms of twistor geometry. Using this twistor space approach, we are able to express the effects of all D-instantons in Type II compactifications concisely as a sum of dilogarithm functions.