We present photoelectron spectroscopy studies on Zn(n) (-) in the size range of n=3-117. We show that zinc clusters exhibit a distinct transition in their electronic structure as a function of size. At small sizes (up to n=18) the clusters follow the Bloch-Wilson picture of the development of a metal from closed-shell atoms, exhibiting a gradual decrease of the gap between the fully occupied s band and the empty p band. For large sizes (n approximately or > 32) the band overlap allows the valence electrons to fully delocalize. This leads to an almost perfect free-electron density of states, as is demonstrated by discussing the spectra in the light of standard free-electron models and by comparison to the results obtained on sodium clusters.