The majority of this chapter (pages 39-56) is set in Gatsby's mansion on a summer evening of the 1920s. The reader can determine this even from the first line of the chapter: "There was music from my neighbors house through the summer nights." Chapter 3 is highly regarded as a perfect example of the recklessness of the "Roaring Twenties." It features one of Jay Gatsby's wild parties during which he, again, tries to attract Daisy to his house across the bay.
Ironically, after the episode at Gatsby's mansion previously described, Nick gives us a clue as to the span of time encompassing the first three chapters:
Reading over what I have written so far, I see I have given the impression that the events of three nights several weeks apart were all that absorbed me. (Fitzgerald 56)
In other words, unless you want to count the very beginning where Nick gives a short version of his life story, our narrator reveals that the first part of the book encompasses three weeks (or approximately one month) of the summer at some point in the early 1920s.
Nick tells us in the beginning of the novel that he went east in the spring of 1922. It took him awhile to find a place to live, get settled in West Egg, and to find his way around. Nick notes that when he left Tom and Daisy's the first night he had dinner with them (Chapter I), "Already it was deep summer . . . ." The three incidents he tells in the first three chapters (dinner at the Buchanans, the party at Tom and Myrtle's apartment, and the party at Gatsby's) took place within a three week period, but it was already "deep summer" before the first one occurred.
At the end of Chapter III, which is set mainly at Gatsby's mansion, Nick says that he "lost sight" of Jordan for a while, but found her again in "midsummer." That suggests July. So, if Nick went east in the spring of 1922 and Chapter III ends in July, then the story he tells to that point must have covered two or three months, depending upon whether spring was April or May.