According to Wikipedia:
The three significant public chess libraries are:
The John G. White Chess and Checkers Collection at Cleveland Public
Library has the largest chess and draughts [chequers for those in the
US] library in the world, with over 32,000 chess books and over 6,000
bound volumes of chess periodicals. It was started with the donation
of a quarter of a million dollars and 11,000 books from John G.
White's private library upon his death.
The Chess & Draughts collection at the Bibliotheca Van der
Linde-Niemeijeriana (part of the Koninklijke Bibliotheek, the National
Library of the Netherlands). The second largest public chess
collection in the world is built on the donations of the private chess
libraries of Antonius van der Linde, Meindert Niemeijer and G.L.
Gortmans. It contains about 30,000 books.
The M.V. Anderson Chess Collection held at State Library Victoria
(Melbourne, Australia) is the largest public chess collection in the
Southern hemisphere. This contains in excess of 12,000 books and many
journal and newsletter titles. Additional titles are added each year.
It is based around M.V. Anderson's personal collection of 6700 volumes
donated between 1959 and 1966.
Grandmaster Lothar Schmid of Bamberg, Germany reportedly owned the
world's largest private collection of chess books and memorabilia. In
1992, Hooper and Whyld stated that Schmid's chess library "is the
largest and finest in private hands, with more than 15,000 items". In
2008, Susan Polgar stated that Schmid "has over 20,000 chess books".
Dirk Jan ten Geuzendam states that Schmid "boasts to have amassed
50,000 chess books.
David DeLucia's chess library contains 7,000 to 8,000 chess books, a
similar number of autographs (letters, score sheets, manuscripts), and
about 1,000 items of "ephemera". DeLucia's library contains such items
as "a 15th-century Lucena manuscript, score-sheets ranging from
Fischer's Game of the Century against Donald Byrne to all the games of
the 1927 New York tournament, eight letters by Morphy, over a hundred
Lasker manuscripts, Capablanca's gold pocket watch, [and] the contract
of the 1886 Steinitz-Zukertort world championship match". Ten
Geutzendam opines that DeLucia's collection "is arguably the finest
chess collection in the world".
Former World Champion Anatoly Karpov has a large chess stamp
collection. He has a private chess library of over 9000 books.