It might not be a Classic at all, as they should have the standard YDDDYNNN 8-digit serial stamped in the back of the headstock along with 'MADE IN USA'. The later Classics (after '92) have a 'Les Paul Classic' decal on the front, rather then 'Les Paul Model' All classics also have the thin taper 60s neck profile.
Is the serial inked or stamped? The current reissues have the serial inked in this manner and the first single digit denotes the model, e.g a 7 for the '57 reissue, an 8 for the '58 reissue, but what a 3 denotes I don't know. Could it be an earlier reissue? You can email Gibson here:
http://www.gibson.com/relations/mailform.html and they should be able to tell you what you need to know.
Good luck,