At the begining of Chapter 7 of The Great Gatsby, explain how Gatsby's "dream" seems to be fading.

Poor Gatsby!  His dream surely is fading by the beginning of Chapter 7, isn't it?  You have to look no further than the first sentence to see the first sign:

It was when curiosity about Gatsby was at its highest that the lights in his house failed to go on one Saturday night--and, as obscurely as it had begun, his career as Trimalchio was over. (Fitzgerald 113)

The parties have ended.  One would assume, at first, that this is because Gatsby has gained the ultimate prize:  Daisy.  However, it isn't long before we learn the truth:

"I hear you fired all your servants."

"I wanted somebody who wouldn't gossip.  Daisy comes over quite often--in the afternoons."

So the whole caravansary had fallen in like a card house at the disapproval in her eyes. (114)

I just love that simile:  that Gatsby's entire entourage had "fallen in like a card house."  Card houses look grand, as if they are full of lots of substance, but give them one slight touch and they fall over, toppling to almost nothing.  Therefore, even worse, Daisy didn't like the way Gatsby was behaving and looked upon his reckless parties of the "Roaring Twenties" with disapproval.  These parties were basically the main method of attracting her attention, so that must have been a blow to him.

The biggest blow, however, comes soon after.  In fact, I wouldn't say that Gatsby's dream truly fades until later in the chapter.  Up until now, there is still the possibility of gaining Daisy's love forever and living together in rich bliss.  But when all of them traverse towards town, Daisy is asked to toe-the-line.  You know what?  She can't.  Gatsby wants nothing less than to have her denounce Tom and admit she never loved him.  That does not happen.

"Oh, you want too much!" she cried to Gatsby.  "I love you now--isn't that enough?  I can't help what's past."  She began to sob helplessly.  "I did love him once--but I loved you too."

Gatsby's eyes opened and closed.

"You loved me too?"  he repeated. (133)

The dream has done more than just "faded" here, it has failed miserably.  Gatsby's physical life may have ended when Tom Wilson took it, but Gatsby's emotional life ended when Daisy screamed that very statement.