Two-photon microscopy is used to image neuronal activity, but has severe limitations for studying deeper cortical layers. Here, we developed a custom three-photon microscope optimized to image a vertical column of the cerebral cortex > 1 mm in depth in awake mice with low (<20 mW) average laser power. Our measurements of physiological responses and tissue-damage thresholds define pulse parameters and safety limits for damage-free three-photon imaging. We image functional visual responses of neurons expressing GCaMP6s across all layers of the primary visual cortex (V1) and in the subplate. These recordings reveal diverse visual selectivity in deep layers: layer 5 neurons are more broadly tuned to visual stimuli, whereas mean orientation selectivity of layer 6 neurons is slightly sharper, compared to neurons in other layers. Subplate neurons, located in the white matter below cortical layer 6 and characterized here for the first time, show low visual responsivity and broad orientation selectivity.