Replacing a magnetic atom by a spinless atom in a heavy-fermion compound generates a quantum state often referred to as a "Kondo-hole". No experimental imaging has been achieved of the atomic- scale electronic structure of a Kondo-hole, or of their destructive impact [Lawrence JM, et al. (1996) Phys Rev B 53:12559-12562] [Bauer ED, et al. (2011) Proc Natl Acad Sci. 108:6857-6861] on the hybridization process between conduction and localized electrons which generates the heavy-fermion state. Here we report visualization of the electronic structure at Kondo-holes created by substituting spinless thorium atoms for magnetic uranium atoms in the heavy-fermion system URu 2Si 2. At each thorium atom, an electronic bound state is observed. Moreover, surrounding each thorium atom we find the unusual modulations of hybridization strength recently predicted to occur at Kondo-holes [Figgins J, Morr DK (2011) Phys Rev Lett 107:066401]. Then, by introducing the "hybridization gapmap" technique to heavy-fermion studies, we discover intense nanoscale heterogeneity of hybridization due to a combination of the randomness of Kondo-hole sites and the long-range nature of the hybridization oscillations. These observations provide direct insight into both the microscopic processes of heavyfermion forming hybridization and the macroscopic effects of Kondo-hole doping.