A chained library is a library where the books are attached to their bookcase by a chain, which is sufficiently long to allow the books to be taken from their shelves and read, but not removed from the library itself. This practice was usual for reference libraries (that is, the vast majority of libraries) from the middle ages to approximately the eighteenth century, as books were extremely valuable during this period. The chains were used to provide sufficient security.
One feature of a chained library that can surprise is that the books are housed with their spine facing away from the reader with only the pages' fore-edges visible (that is, the 'wrong' way round to people accustomed to contemporary libraries). This is so that each book can be removed and opened without needing to be turned around, hence avoiding tangling its chain.
External links
The Mappa Mundi and Chained Library at Hereford Cathedral