When was the city of Kiev founded?

"The History of Kiev (also spelled Kyiv as per Ukrainian: Київ), the largest city and the capital of Ukraine, is long and remarkable. The exact time of city foundation is hard to determine. The legend has it that the emergence of the great city on the future location of Kiev was prophesied by St. Andrew (d. AD 60/70) fascinated by the spectacular location on the hilly shores of the Dnieper river. The city is thought to have existed as early as the 6th century, initially as a Slavic settlement. Gradually acquiring the eminence as the center of the East Slavic civilization, Kiev reached its Golden Age as the center Kievan Rus' in the tenth–twelfth centuries. Its political, but not cultural, importance started to decline somewhat when it was completely destroyed during the Mongol invasion in 1240. In the following centuries Kiev was a provincial capital of marginal importance in the outskirts of the territories controlled by its powerful neighbors: the Grand Duchy of Lithuania, the Polish-Lithuanian Commonwealth and the Muscovite Russia, later the Russian Empire. A Christian city since 988, it still played an important role in preserving the traditions of Orthodox Christianity, especially at times of domination by Catholic Poland, and later the atheist Soviet Union."

"According to a legend, Kiev was founded in the 5th century by East Slavs. The legend of Kyi, Schek and Khoryv speaks of a founder-family consisting of a Slavic tribe leader Kyi, the eldest, his brothers Schek and Khoriv, and also their sister Lybid, who founded the city. Kyiv/Kiev is translated as "belonging to Kyi".

The non-legendary time of the founding of the city is harder to ascertain. Scattered Slavic settlements existed in the area from the 6th century, but it is unclear whether any of them later developed into the city. Eighth century fortifications were built upon a Slavic settlement apparently abandoned some decades before[1]. It is unclear whether these fortifications were built by the Slavs or the Khazars. If it's the former, it is also uncertain when Kiev fell under the rule of the Khazar empire and whether the city was founded by the Khazars. However, the Primary Chronicle (a main source of information about the early history of the area) mentions Slavic Kievans telling Askold and Dir that they live without a local ruler and pay a tribute to Khazars in an event attributed to the 9th century. At least during the 8th and 9th centuries Kiev functioned as an outpost of the Khazar empire. A hill-fortress, called Sambat (Old Turkic for "High Place") was built to defend the area.

At some point during the late ninth or early tenth century Kiev fell under the rule of Varangians (see Askold and Dir, and Oleg of Novgorod) and became the nucleus of the Rus' polity. The date given for Oleg's conquest of the town in the Primary Chronicle is 882, but some historians, such as Omeljan Pritsak and Constantine Zuckerman, dispute this and maintain that Khazar rule continued as late as the 920s (documentary evidence exists to support this assertion — see the Kievian Letter and Schechter Letter.) Other historians suggest that the Magyar tribes ruled the city between 840 and 878, before migrating with some Khazar tribes to Hungary"
Source and further information:
http://en.wikipedia.org/wiki/History_of_Kiev

I am not sure when but I am sure you can find this info on the Net- just have to research. :)