The design and first stage of construction of a reinforced concrete public building in Florence, seismically protected by a combined base isolation/supplemental damping system, where silicone-fluid viscous spring-dampers are coupled with steel-Teflon sliding bearings, are presented in this paper. The design represents the first application in Italy and Europe of this special passive control strategy, which has been for many years the object of research studies by the authors, also developed within EC-funded Research Projects.