Fundamental studies of intrinsic charge transport properties of organic semiconductors are often hindered by charge traps associated with static disorder present even in optimized single-crystal devices. Here, we report a method of surface functionalization using an inert non-conjugated polymer, perfluoropolyether (PFPE), deposited at the surface of organic molecular crystals, which results in accumulation of mobile holes and a 'trap healing' effect at the crystal/PFPE interface. As a consequence, a remarkable ultralow-noise, trp-free conduction regime characterized by intrinsic mobility and transport anisotropy emerges in organic single crystals, and Hall effect measurements with an unprecedented signal-to-noise ratio are demonstrated. This general method to convert trap-dominated organic semiconductors to intrinsic systems may enable the determination of intrinsic transport parameters with high accuracy and make Hall effect measurements in molecular crystals ubiquitous.