The challenge is how to divide the city between the two sides. Back in 2000, then-President Clinton came up with some parameters for how to do it: areas populated mostly by Jews would remain Israeli; those populated mostly by Arabs would become the new Palestinian capital. That meant that for the most part East Jerusalem would go to the Arabs.
Well, it's not so simple anymore. In the decade that has elapsed, more and more Israeli settlers have moved east into the Arab-populated areas. One place where it has gotten especially complicated - and volatile - is the Arab neighborhood of Silwan.
The complication in Silwan involves an Israeli archeological dig called the "City of David."
It's a sacred city to the world but also a place where science and faith sometimes collide. Can archeology prove the Bible?
Extra: Touring East Jerusalem
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Link: City of David
Link: Silwan Information Center
Go to Jerusalem today and you'll likely visit the City of David, one of the world's great archeological wonders, where diggers are sifting back through time: scores of workers, filling hundreds of buckets, unearthing thousands of years.
"This tunnel is 3800 and 50 years old," Doron Spielman, the site's international director of development, told correspondent Lesley Stahl as he led her through an ancient tunnel.
According to Spielman, the tunnel is exactly as it was when it was built. "Look at these stones, you can see the chisel marks on the walls," he pointed out.
He then took her to another area aboveground. "This is the original flooring. These are more ritual baths or water cisterns," he pointed out.
Spielman led us down to an ancient waterway carved out of the hard stone. "The whole beginning of life in ancient Jerusalem happened from this little spring which is nestled in this little cave," he explained.
We were taken down excavated tunnels no human eye has seen for two millennia and shown the process of removing the layers of history - sandbag by sandbag - from when the city was sacked by the Romans, and before them the Babylonians.
"So this structure was here when Abraham was here?" Stahl asked.
"That's right. He saw it with his own eyes," Spielman said.
That's a bit of a stretch: archeologists tell us that no one has found any evidence that Abraham was ever there. It's controversial that the City of David uses discoveries to try to confirm what's in the Bible, particularly from the time of David, the king who made Jerusalem his capital.
"People believe that when King David captured the city, he snuck underground through this tunnel which led him underneath the city wall, up into the city," Spielman said.
Half a million tourists visit the site every year, with guides who try to bring King David to life. There's an implicit message: that because David conquered the city for the Jews back then, Jerusalem belongs to the Jews today.
"Today, I've seen scores and scores of soldiers coming through," Stahl remarked.
"It's part of their cultural day to try to learn about what they're fighting for. And when we bring them here they understand that they're not just fighting for today, they actually represent the return of the Jewish people to Israel after thousands of years," Spielman said.
"So archeology is being used as a political tool. I mean, I hate to use the word, but indoctrination almost," Stahl replied.
"I wouldn't call it indoctrination. I would call it giving meaning to life, giving meaning to why we're here," he replied.
But for all the talk of King David, one thing is glaringly missing here at the City of David.
"There's actually no evidence of David, right?" Stahl asked.
"There's no doubt that this is the City of David from the Bible. There's no doubt that the Bible took place here. Proof of David himself, until we find the actual name, we can't say," Spielman acknowledged.
Another problem is an inconvenient truth: that biblical Jerusalem is not located in the western half of the city. It's right under the densely populated Arab neighborhood of Silwan. And according to the Clinton parameters, Silwan should be part of a Palestinian state.
To remedy that, organizations that move Jewish settlers into Arab areas have infiltrated Silwan.
For example, a group of settlers live in a seven-story building under heavy security. They've barricaded themselves in and refuse to leave. With some 450 Jews living among tens of thousands of Arabs, Silwan is now at the center of the battle to keep all of Jerusalem under Israeli control.