Intelligent surfaces comprising of cost effective, nearly pas- sive, and reconfigurable unit elements are lately gaining in- creasing interest due to their potential in enabling fully pro- grammable wireless environments. They are envisioned to offer environmental intelligence for diverse communication objectives, when coated on various objects of the deployment area of interest. To achieve this overarching goal, the chan- nels where the Reconfigurable Intelligent Surfaces (RISs) are involved need to be in principle estimated. However, this is a challenging task with the currently available hardware RIS ar- chitectures requiring lengthy training periods among the net- work nodes utilizing RIS-assisted wireless communication. In this paper, we present a novel RIS architecture comprising of any number of passive reflecting elements, a simple con- troller for their adjustable configuration, and a single Radio Frequency (RF) chain for baseband measurements. Capitaliz- ing on this architecture and assuming sparse wireless channels in the beamspace domain, we present an alternating optimiza- tion approach for explicit estimation of the channel gains at the RIS elements attached to the single RF chain. Represen- tative simulation results demonstrate the channel estimation accuracy and achievable end-to-end performance for various training lengths and numbers of reflecting unit elements.