By exploiting the quantised nature of light, we demonstrate a sub-shot-noise scanning optical transmittance microscope. Our microscope demonstrates, with micron scale resolution, a factor of improvement in precision of 1.76(9) in transmittance estimation gained per probe photon relative to the theoretical model, a shot-noise-limited source of light, in an equivalent single-pass classical version of the same experiment using the same number of photons detected with a 90% efficient detector. This would allow us to observe photosensitive samples with nearly twice the precision, without sacrificing image resolution or increasing optical power to improve signal-to-noise ratio. Our setup uses correlated twin-beams produced by parametric down-conversion, and a hybrid detection scheme comprising photon-counting-based feed-forward and a highly efficient CCD camera.