Glasses are lucrative engineering materials owing to their superior mechanical properties such as high strength and large elastic strain. A central question concerns incipient plasticity - the onset of permanent deformation - that is central to their relaxation, aging, yield and fracture. Here, we use an analogue of nano-indentation performed on a colloidal glass to obtain direct images of the incipient plasticity, allowing us to elucidate the onset of permanent deformation. We visualize the microscopic strain by following distorted nearest neighbor configurations, and observe a surprising hierarchical structure of deformation: at the onset of irreversible deformation, the strain acquires a robust fractal structure, and we measure its fractal dimension. These results give direct evidence that the onset of permanent deformation has the hallmarks of a critical point, in agreement with recent theoretical works.