We report the observation of the b-->d penguin-dominated decay B;{0}-->K;{*0}K[over ];{*0} with a sample of 383.2+/-4.2 million BB[over ] pairs collected with the BABAR detector at the PEP-II asymmetric-energy e;{+}e;{-} collider at the Stanford Linear Accelerator Center. The measured branching fraction is B(B;{0}-->K;{*0}K[over ];{*0})=[1.28_{-0.30};{+0.35}+/-0.11]x10;{-6} and the fraction of longitudinal polarization is f_{L}(B;{0}-->K;{*0}K[over ];{*0})=0.80_{-0.12};{+0.10}+/-0.06. The first error quoted is statistical and the second systematic. We also obtain an upper limit at the 90% confidence level on the branching fraction for B(B;{0}-->K;{*0}K;{*0})<0.41x10;{-6}.