We report for the first time on a hole conductor-free mesoscopic methylammonium lead iodide (CH3NH3PbI3) perovskite/TiO2 heterojunction solar cell, produced by deposition of perovskite nanoparticles from a solution of CH3NH3I and PbI2 in gamma-butyrolactone on a 400 nm, thick film of TiO2 (anatase) nanosheets exposing (001) facets. A gold film was evaporated on top of the CH3NH3PbI3 as a back contact. Importantly, the CH3NH3PbI3 nanoparticles assume here simultaneously the roles of both light harvester and hole conductor, rendering superfluous the use of an additional hole transporting material. The simple mesoscopic CH3NH3PbI3/TiO2 heterojunction solar cell shows impressive photovoltaic performance, with short-circuit photocurrent J(sc) = 16.1 mA/cm(2), open-circuit photovoltage V-oc = 0.631 V, and a fill factor FF = 0.57, corresponding to a light to electric power conversion efficiency (PCE) of 5.5% under standard AM 1.5 solar light of 1000 W/m(2) intensity. At a lower light intensity of 100W/m(2), a PCE of 7.3% was measured. The advent of such simple solution-processed mesoscopic heterojunction solar cells paves the way to realize low-cost, high-efficiency solar cells.