That said, according to MSN Encarta the Chicago Public Library is third for all U.S. Libraries. Because, the Library of Congress and Harvard University libraries are statistically ranked by the Association of Research Libraries and Chicago is ranked by Public Library Data Service, Chicago considers itself the largest.
Thus you get the following ranking. Largest U.S. Libraries
I checked some other listings (including yours) and the rankings are all over the map. It's a conspiracy.
Here's some library trivia while we are on the subject:
The St. Phillips Church Parsonage Provincial Library, established in 1698 in Charleston, South Carolina, was the first public lending library in the American Colonies.