The American Dream
The American Dream in Chinatown is really an American Nightmare: instead of white picket fences, it's corpses in dry riverbeds. Instead of a two-car garage and 2.2 children, it's incest babies and murder. Instead of Norman Rockwell, it's Hieronymos Bosch.
We don't see anyone achieving their romantic aspirations in this movie—no aspiring Hollywood actors or L.A. new age entrepreneurs. There's just a government bureaucracy controlled by a malevolent old tycoon who's busily exploiting a city and stealing its water supply for profit.
And the entire populace—with the exception of Jake Gittes—is totally blind and oblivious to all of this.
In Chinatown, we see a trippy photonegative version of the American Dream. We don't see middle-class people leading enjoyable suburban dream lives. We see a super-rich guy, Noah Cross, devouring the economy with the help of a bunch of henchmen like Claude Mulvihill and willing white-collar drones like Russ Yelburton.
People lower down on the economic scale, like the prostitute Ida Sessions, end up getting used (and/or killed). And the old people in the retirement home who unwittingly cover up Noah's water-theft scheme? They're being gamed too. If the American Dream is dead, Noah and his boys are the worms eating its corpse.
All that the hero, Jake, can do is try to help Evelyn escape the horror of life with her father—and he even fails at that. He has no aspirations towards the American Dream of his own that we see, no house on the hill he's striving for.
Aside from trying to save the innocent, Jake's one motive is survival. He's like a more desperate, less-physically-skilled Bear Grylls.