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Quick Answer.  Noble gases are unreactive because their outer electron shells are full and therefore in their most stable state. Normally, elements react with one another because they have incomplete electron shells. They lose, gain or share electrons in order to gain a more stable electron configuration.
The properties of the noble gases can be well explained by modern theories of atomic structure: their outer shell of valence electrons is considered to be full, giving them little tendency to participate in chemical reactions. See: Noble gas.