Observation of the Decay<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">B</mml:mi><mml:mspace/><mml:mo>→</mml:mo><mml:mspace/><mml:mi mathvariant="italic">K</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">l</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">l</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>

We report a search for the flavor-changing neutral current decay $B\ensuremath{\rightarrow}{K}^{(*)}{l}^{+}{l}^{\ensuremath{-}}$ using a $29.1{\mathrm{fb}}^{\ensuremath{-}1}$ data sample accumulated at the $\ensuremath{\Upsilon}(4S)$ resonance with the Belle detector at the KEKB ${e}^{+}{e}^{\ensuremath{-}}$ storage ring. We observe the decay process $B\ensuremath{\rightarrow}{\mathrm{Kl}}^{+}{l}^{\ensuremath{-}}(l\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}e,\ensuremath{\mu})$, for the first time, with a branching fraction of $B(B\ensuremath{\rightarrow}{\mathrm{Kl}}^{+}{l}^{\ensuremath{-}})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}({0.75}_{\ensuremath{-}0.21}^{+0.25}\ifmmode\pm\else\textpm\fi{}0.09)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$.