RSS-based indoor positioning is a consolidated research field for which several techniques have been proposed. Among them, Bluetooth Low Energy (BLE) beacons are a popular option for practical applications. This paper presents a new BLE RSS database that was created to aid in the development of new BLE RSS-based positioning methods and to encourage their reproducibility and comparability. The measurements were collected in two university zones: an area among bookshelves in a library and an area of an office space. Each zone had its own batch of deployed iBKS 105 beacons, configured to broadcast advertisements every 200 ms. The collection in the library zone was performed using three Android smartphones of different brands and models, with beacons broadcasting at −12 dBm transmission power, while in the other zone the collection was performed using of one those smartphones with beacons configured to advertise at the −4 dBm, −12 dBm and −20 dBm transmission powers. Supporting materials and scripts are provided along with the database, which annotate the BLE readings, provide details on the collection, the environment, and the BLE beacon deployments, ease the database usage, and introduce the reader to BLE RSS-based positioning and its challenges. The BLE RSS database and its supporting materials are available at the Zenodo repository under the open-source MIT license.