ANSWER
Venice
In 1516 the city required its Jews to live a small walled and gated area in the north of Venice called the "Ghetto Nuovo". During the day they were free to move about the city, engaged in one of the handful of professions legally allotted them (pawnbroker, moneylender, merchant, doctor, etc.), provided they wore a yellow badge or scarf identifying themselves as Jews. At night they were required to return to the ghetto where the gates would be locked behind them. As the Jewish population increased, the ghetto was expanded. First in 1541 to include the "Ghetto Vecchio" and again in 1633 to include the "Ghetto Nuovissimo". This system continued until Napoleon conquered the city in 1797. In Venice, as he would do in other cities, Napoleon tore down the gates of the ghetto and gave the Jews an equal standing in their community.
The word "ghetto" comes from the Venetian word "geto", meaning foundry. Prior to becoming an exclusively Jewish neighborhood, the Venice ghetto was the site of two foundries ("ghetto vecchio", the old foundry, and "ghetto nuovo", the new foundry).
(Honorable mention to everyone who mentioned that the "Land of Goshen" was the first area that we would today consider a ghetto, even though Goshen pre-dates the word "ghetto" by several millennia.)
WHO GOT IT RIGHT: JP Weigt, Ryan Scannell, Bob Milligan, Robin Campbell, Christine Severen, Mark Collins, Robert Walker, Marc Quinlivan, Brian Bement, Peter Phelan, G Hill, and Andie J.