Ligand-protected Au clusters are non-bleaching fluorescence markers in bio- and medical applications. Here we show that their fluorescence can be an intrinsic property of the Au cluster itself. We find a very intense and sharp fluorescence peak located at lambda = 739.2 nm (1.68 eV) for Au-20 clusters in a Ne matrix held at 6 K. The fluorescence reflects the Highest Occupied Molecular Orbital-Lowest Unoccupied Molecular Orbital (HOMO-LUMO) diabatic bandgap of the cluster. Au-20 shows a very rich absorption fine structure reminiscent of well defined molecule-like quantum levels. These levels are resolved since Au-20 has only one stable isomer (tetrahedral); therefore our sample is mono-disperse in cluster size and conformation. Density-functional theory (DFT) and time-dependent DFT calculations clarify the nature of optical absorption and predict both main absorption peaks and intrinsic fluorescence in fair agreement with experiment. Published by AIP Publishing.