LUKE: I’ll be home early, anything besides the Q-Tips?
LORELAI: Um, cotton balls, world peace, Connie Chung’s original face back.
Constance “Connie” Chung (born 1946), journalist who has been an anchor and reporter with many major news networks. In June 2002 she began hosting her own show on CNN, called Connie Chung Tonight. Although it had moderate ratings, it was cancelled the following year when the Iraq War broke out, and Chung was needed as a reporter.
Presumably Lorelai has been watching the show over the summer in her lonely hours, and dislikes the amount of cosmetic interventions Connie Chung has had done since she last noticed her. There were numerous references in the show to Lorelai not approving of cosmetic surgery – which in retrospect seem rather ironic after watching Lauren Graham in A Year in the Life.
The Annotated Gilmore Girls 