The highest point you have a chance of getting to in the Chrysler Building is the 71st floor—that floor used to be the home of a public viewing gallery, but that closed in 1945. Currently it houses office space, and is the highest-occupied floor. But what's above that?
"Above the 71st floor, the stories of the building are designed mostly for exterior appearance, functioning mainly as landings for the stairway to the spire. Very narrow with low, sloped ceilings, these top stories are useful only for holding radio-broadcasting and other mechanical and electrical equipment."
And above that is the spire itself. Recently urban explorer Moses Gates (filmed by Opie of The Opie & Anthony Show) navigated through a series of ladders in the close quarters to get up to the tippy top—and you can see it all through their lens in the below video:
Here's another great story about a journey up the spire—from a man who has been to "the extreme tip (1,046 feet 4 inches)" he says there is "One word—peace."
Some more fun facts about the Chrysler Building can be found here—like how the spire was delivered in four sections, and on October 23rd, 1929 the bottom section was hoisted onto the top of the building's dome and lowered into the 66th floor. The remaining sections were then brought up and riveted to the first one in sequential order. And all this took just 90 minutes! [via Reddit]