Within a Kondo lattice, the strong hybridization between electrons localized in real space (r-space) and those delocalized in momentum-space (k-space) generates exotic electronic states called 'heavy fermions'. In URu(2)Si(2) these effects begin at temperatures around 55 K but they are suddenly altered by an unidentified electronic phase transition at T(o) = 17.5 K. Whether this is conventional ordering of the k-space states, or a change in the hybridization of the r-space states at each U atom, is unknown. Here we use spectroscopic imaging scanning tunnelling microscopy (SI-STM) to image the evolution of URu(2)Si(2) electronic structure simultaneously in r-space and k-space. Above T(o), the 'Fano lattice' electronic structure predicted for Kondo screening of a magnetic lattice is revealed. Below T(o), a partial energy gap without any associated density-wave signatures emerges from this Fano lattice. Heavy-quasiparticle interference imaging within this gap reveals its cause as the rapid splitting below T(o) of a light k-space band into two new heavy fermion bands. Thus, the URu(2)Si(2) 'hidden order' state emerges directly from the Fano lattice electronic structure and exhibits characteristics, not of a conventional density wave, but of sudden alterations in both the hybridization at each U atom and the associated heavy fermion states.