Wow. In my opinion you have chosen the chapter that has the very least amount of memorable quotes from this iconic novel. (Ha!) I loved this task just because it wasn't as easy as it could have been. I agree with the above posters that many of the good quotes from this chapter would refer to the recklessness of the Roaring Twenties or of the gossip about Gatsby, ... but instead, I have chosen an important instance of foreshadowing:
A sudden emptiness seemed to flow now from the windows and the great doors, endowing with complete isolation the figure of the host, who stood on the porch, his hand up in a formal gesture of farewell.
Ah, the emptiness after a full night of drunken revelry all with an ulterior motive. Gatsby: isolated in life, isolated in death. No real love in sight, ... not from Daisy, ... not even from the non-existent guests at his funeral. Poor guy.
The quotes the first two posters gave are great. I have another that could be in the running for an important quote in chapter 3.
"[Gatsby's smile had] a quality of eternal reassurance in it, that you may come across four or five times in life....It understood you just as far as you wanted to be understood, believed in you as you would like to believe in yourself." Chapter 3, pg. 48
In my opinion this kind of sums up not only Gatsby's charming ways with people, but the superficial nature of society in the 20's. It seems to say that there was so little human connection in this "me" generation of parties and alcohol, that a sweet smile from Gatsby was a rarity and something to be noted.
It also helps us understand Nick's quote later in the novel when he shouts across the lawn that "Gatsby is worth more than the whole damn bunch put together". Despite his shady dealings, Nick found a real human quality in Gatsby that wasn't found in many other places.
Fitzgerald's satire is evident in his depiction of Jordan Baker in Chapter Three. Coinciding with the motif of superficiality of the people who attend Gatsby's parties, Jordan changes the subject of conversation of some guests about Gatsby who discuss whether he attended Oxford.
"Anyhow he gives large parties," said Jordan, changing the subject with an urban distaste for the concrete. "And I like large parties. They're so intimate. At small parties there isn't any privacy."
There are quite a few quotes that you could say are important. I like the one in the first post and I think that the post does a good job of explaining why it is important.
For another aspect of the chapter, I'd offer this quote:
“Gatsby. Somebody told me ——”
The two girls and Jordan leaned together confidentially.
“Somebody told me they thought he killed a man once.”
A thrill passed over all of us. The three Mr. Mumbles bent forward and listened eagerly.
“I don’t think it’s so much THAT,” argued Lucille sceptically; “it’s more that he was a German spy during the war.”
One of the men nodded in confirmation.
“I heard that from a man who knew all about him, grew up with him in Germany,” he assured us positively.
“Oh, no,” said the first girl, “it couldn’t be that, because he was in the American army during the war.” As our credulity switched back to her she leaned forward with enthusiasm. “You look at him sometimes when he thinks nobody’s looking at him. I’ll bet he killed a man.”
I think that it is very important to realize what a mystery Gatsby is. No one really knows who he is. This is a big deal in the book -- how did Gatsby get him money? How dangerous is he? What sorts of lengths would he go to to get what he wants? This is the sort of thing you wonder in this chapter and the quote above shows that idea.
You might receive many different answers to this question, as in reality, there is no one important quote in this chapter. However, to me, one of the important quotes that it is important to focus on is the description of the revelers at Gatsby's parties and how they are presented. Note what the text tells us about them:
I believe that on the first night I went to Gatsby's house I was one of the few guests that had actually been invited. People were not invited--they went there. They got into automobiles which bore them out to Long Island, and somehow they ended up at Gatsby's door. Once they were introduced by somebody who knew Gatsby, and after that they conducted themselves according to the rules of behaviour associated with an amusement park.
Note the impression of the rich and famous that this description gives. In an era of Prohibition, which was characterised by sobriety and want and making ends meet, the rich were able to carry on regardless and engage in riotous events involving excess and the illegal consumption of alcohol. In particular, their moral behaviour is referenced disparagingly, as they behaved like they were in "an amusement park." This quote also foreshadows the lack of personal connection that these revelers had with Gatsby himself, which of course prepares us for his ultimately friendless end.