[X] = Read It.
[-] = Refuse to read it.
[L] - Local library has it.
Chandler's library actually has a lot more of these than I thought they would, but most of the ones they're missing are they ones I'm more likely to like (50s and 60s era stuff).
[ ] ... And Call Me Conrad by Roger Zelazny, 1966 (tie)
[X] A Canticle for Leibowitz by Walter M. Miller, Jr., 1961
[ ] A Case of Conscience by James Blish, 1959
[L] A Deepness in the Sky by Vernor Vinge, 2000
[L] A Fire Upon the Deep by Vernor Vinge, 1993 (tie)
[-] American Gods by Neil Gaiman, 2002
[ ] Barrayar by Lois McMaster Bujold, 1992
[L] Blue Mars by Kim Stanley Robinson, 1997
[ ] Cyteen by C. J. Cherryh, 1989
[L] Doomsday Book by Connie Willis, 1993 (tie)
[L] Double Star by Robert A. Heinlein, 1956
[L] Downbelow Station by C. J. Cherryh, 1982
[ ] Dreamsnake by Vonda McIntyre, 1979
[X] Dune by Frank Herbert, 1966 (tie)
[X] Ender's Game by Orson Scott Card, 1986
[L] Farmer in the Sky by Robert A. Heinlein, 1951
[X] Foundation's Edge by Isaac Asimov, 1983
[X] Forever Peace by Joe Haldeman, 1998
[L] Gateway by Frederik Pohl, 1978
[L] Green Mars by Kim Stanley Robinson, 1994
[-] Harry Potter and the Goblet of Fire by J. K. Rowling, 2001
[L] Hyperion by Dan Simmons, 1990
[L] Lord of Light by Roger Zelazny, 1968
[L] Mirror Dance by Lois McMaster Bujold, 1995
[L] Neuromancer by William Gibson, 1985
[X] Rendezvous with Rama by Arthur C. Clarke, 1974
[X] Ringworld by Larry Niven, 1971
[-] Speaker for the Dead by Orson Scott Card, 1987
[ ] Stand on Zanzibar by John Brunner, 1969
[L] Starship Troopers by Robert A. Heinlein, 1960
[L] Startide Rising by David Brin, 1984
[X] Stranger in a Strange Land1 by Robert A. Heinlein, 1962
[ ] The Demolished Man by Alfred Bester, 1953
[L] The Diamond Age by Neal Stephenson, 1996
[X] The Dispossessed by Ursula K. Le Guin, 1975
[X] The Forever War2 by Joe Haldeman, 1976
[L] The Fountains of Paradise by Arthur C. Clarke, 1980
[X] The Gods Themselves by Isaac Asimov, 1973
[X] The Left Hand of Darkness by Ursula K. Le Guin, 1970
[X] The Man in the High Castle by Philip K. Dick, 1963
[X] The Moon Is a Harsh Mistress by Robert A. Heinlein, 1967
[X] The Mule by Isaac Asimov, 1946
[ ] The Snow Queen by Joan D. Vinge, 1981
[L] The Uplift War by David Brin, 1988
[L] The Vor Game by Lois McMaster Bujold, 1991
[ ] The Wanderer by Fritz Leiber, 1965
[ ] They'd Rather Be Right by Mark Clifton and Frank Riley, 1955
[L] To Say Nothing of the Dog by Connie Willis, 1999
[ ] To Your Scattered Bodies Go by Philip José Farmer, 1972
[ ] Way Station by Clifford D. Simak, 1964
[ ] Where Late the Sweet Birds Sang by Kate Wilhelm, 1977
1: I should probably note that the edition I read was the 1991 uncut version (which had, if I recall correctly, about 250,000 words worth of story that were cut to ease the publisher's concerns about the content.
2: Similarly, the version of The Forever War which I've read is the "Author's Preferred Edition", which (if I understand correctly) has an entirely different Part Two and some other differences in the other Parts.