The immortality of the 1920's and the American Dream are shown subtly in this chapter.
American Dream - Gatsby explained to Nick about the time before the war, he said, "I lived like a young rajah in all the capitals of Europe - Paris, Venice, Rome - collecting jewels, chiefly rubies, hunting big game, painting a little, things for myself only, and trying to forget something very sad that had happened long ago." (pg.70) This shows how Gatsby was somewhat living the dream, he was traveling and living without a care. He was filthy rich, young, and living extravagantly. He becomes a decorated war hero, representing bravery and integrity and all things "American." Then later on in the chapter, as Gatsby and Nick are driving, Nick describes the city "in its first wild promise of all the mystery and the beauty in the world." (pg. 73) This shows why people, including Nick, moved out east. For the lure of the American Dream and the promise of wealth and adventure. But this quote also gives the connotation that that's not what the city is; that there's a deeper, darker truth within its streets.
Immortality - There are little things that show the immortality, for example, Gatsby used his connections and past to get out of a simple ticket. And we also meet a man, Mr. Wolfsheim, a man who turns out to be a gambler who fixed the 1919 World Series. It would have been distasteful to have interacted with a man of such sorts, but Gatsby reveres him and finds him good company. Wolfsheim assumes Nick is a man who wants to do business, and we see a glimpse of an abruptness in him. When he learns of his mistake, he relaxes and continues merrily. To me, this shows how underneath the easy-going, care free of the 20's there was corruption and crime - and the two were intertwined.