Which third would that be?
That is a really tough question. I'll speculate but it isn't much more than that. The difficulty is that Rand tends to make the same point several different ways, each of which is pretty good. From the point of view of the author, for whom each of the different ways might be the only one that turns a light bulb on for the reader, there is a resistance to cutting any of them. For the editor, who has to sell the thing in a package that book stores will buy, it simply has to be smaller. In fact, AS almost didn't get published for that very reason - the editor who finally bought it had to threaten to quit in order to convince his superiors to go through with it. And for the reader contemplating an 1100-page brick it's pretty intimidating.
What I'd cut at this point might be some of the unneccessarily (IMHO) repetitive descriptions of Hank and Lillian's married life and perhaps the irritatingly theoretical explanations for why Dagny and Hank wind up sharing a bed. And some of the speeches seem artificially long - did Francisco really need upwards of five pages to make his Root Of Money point? And does anyone really think that a crowd at a wedding party would listen to it?
The real problem, I think, is that Rand was trying to balance a flow of logic with a flow of narrative and the two aren't always compatible. What the heck, I might change my mind a few chapters hence...