LORELAI: Is this a setup?
LORELAI: Uh, Connecticut Ken in there, is he my invited escort for the evening?
Ken is a toy doll introduced by Mattel in 1961 as a male counterpart to Barbie; he also has multiple fashion accessories. Barbie and Ken are promoted as a couple, although sometimes they just seem to be good friends – with the result that Ken is sometimes jokingly rumoured to be gay.
To call a man a “Ken Doll” is generally an insult. It might suggest he is handsome but shallow and boring, or that he exists only to serve as an escort or accessory to a woman. Lorelai is probably implying both these things by calling Chase “Connecticut Ken”.