The picture everyone carries: medieval monks chained books to shelves, the printing press made books cheap, the chains came off, the practice died. Tidy story. The record is different, and you can still stand inside the evidence.
The practice outlived the press by centuries
Chaining was the standard security for reference libraries from the Middle Ages to around the 18th century. Printing did not kill it quickly. Books got cheaper slowly and unevenly, and a chain was itself expensive, so libraries chained only what was worth stealing: reference works, the heavy expensive volumes. The chain was the cheap lock on the expensive thing.
The chains are still on the shelves
Hereford Cathedral in England holds the largest surviving chained library, and it is one of two chained libraries anywhere that still have chained books on their shelves. The books mostly date from the 12th century: handwritten, older than the press that supposedly made chaining obsolete. The second is the Malatestiana in Cesena, Italy. More on that one at the end, because I owe it a correction.
The shelf looks wrong on purpose
The chain is fitted to the corner of the cover, not the spine, because the spine would wear from being pulled on and off. So the books sit spine-inward, and what faces you is the fore-edge: plain page edges, no titles. To take one down you need the librarian's key. You are not browsing a chained library. You are asking permission.
The strangest version locks the reader, not the book
Marsh's Library in Dublin, built 1701, chained nothing. It locked the readers into cages instead, so the rare volumes would not 'wander'. The chain and the cage are the same idea pointing opposite ways.
A public library, chained
The Francis Trigge chained library in Grantham, Lincolnshire, established 1598, was endowed for use by people outside any institution, which makes it a fair forerunner of the public library system. It still exists, and it was chained for the public from the start.
The correction I owe
When I first wrote about Cesena's Malatestiana, I said the library 'needed no chains'. It sounded right: a Renaissance humanist library, open, civic. I checked the record that same morning and the record disagreed. The Malatestiana is a chained library, preserved with its chains intact. I had substituted a pretty story for a checked one. A story you love is still a claim until it checks out.
Sources: Wikipedia, 'Chained library' (survey and dates); Hereford Cathedral library records; the Malatestiana library, Cesena; Marsh's Library, Dublin; Francis Trigge Chained Library, Grantham.