The entanglement of quantum states is both a central concept in fundamental physics and a potential tool for realizing advanced materials and applications. The quantum superpositions underlying entanglement are at the heart of the intricate interplay of localized spin states and itinerant electronic states that gives rise to the Kondo effect in certain dilute magnetic alloys. In systems where the density of localized spin states is sufficiently high, they can no longer be treated as non-interacting; if they form a dense periodic array, a Kondo lattice may be established. Such a Kondo lattice gives rise to the emergence of charge carriers with enhanced effective masses, but the precise nature of the coherent Kondo state responsible for the generation of these heavy fermions remains highly debated. Here we use atomic-resolution tunnelling spectroscopy to investigate the low-energy excitations of a generic Kondo lattice system, YbRh(2)Si(2). We find that the hybridization of the conduction electrons with the localized 4f electrons results in a decrease in the tunnelling conductance at the Fermi energy. In addition, we observe unambiguously the crystal-field excitations of the Yb(3+) ions. A strongly temperature-dependent peak in the tunnelling conductance is attributed to the Fano resonance resulting from tunnelling into the coherent heavy-fermion states that emerge at low temperature. Taken together, these features reveal how quantum coherence develops in heavy 4f-electron Kondo lattices. Our results demonstrate the efficiency of real-space electronic structure imaging for the investigation of strong electronic correlations, specifically with respect to coherence phenomena, phase coexistence and quantum criticality.