In Chapter I of The Great Gatsby, what distinguished club is Nick talking about?
Nick's reference, actually, is to a "secret society," and it is found in a passage while Nick and Daisy are talking alone. Daisy has explained to Nick the various ways her life is quite awful; her outburst seems heartfelt and filled with emotion. However, as soon as she stops speaking, Nick feels "the basic insincerity of what she had said." He is suddenly uneasy in Daisy's company, feeling "the whole evening had been a trick" to manipulate his emotions:
I waited, and sure enough, in a moment she looked at me with an absolute smirk on her lovely face as if she had asserted her membership in a rather distinguished secret society to which she and Tom belonged.
Nick's reference to "a rather distinguished secret society" is not clarified at this point in the novel, but it is important because it represents the first time he becomes aware of Daisy's shallow and disingenuous personality and the bond that holds the Buchanans together--Tom and Daisy both "belong" to an as yet unnamed group of "distinguished" people who are set apart from society at large. The connotation of "secret society" suggests limited membership and special rules of behavior. In spotting Daisy's phoniness and manipulation, Nick feels a very distinct difference between her (and Tom) and himself. As the novel develops, this difference becomes clear to Nick. He develops contempt for the Buchanans and their "secret society," the idle, snobbish, selfish upper class of inherited wealth and amoral, destructive behavior.