Single crystals of hybrid perovskites have shown remarkably improved physical properties compared to their polycrystalline film counterparts, underscoring their importance in the further development of advanced semiconductor devices. Here we present a new method of sizeable CH3NH3PbCl3 single crystal growth based on retrograde solubility behavior of hybrid perovskites. We show, for the first time, the energy band structure, charge-carrier recombination and transport properties of single crystal CH3NH3PbCl3. The chloride-based perovskite crystals exhibit trap-state density, charge carriers concentration, mobility and diffusion length comparable with the best quality crystals of methylammonium lead iodide or bromide perovskites reported so far. The high quality of the crystal along with its suitable optical bandgap enabled us to design and build an efficient visible-blind UV-photodetector, demonstrating the potential of this material to be employed in optoelectronic applications.