  We search for the rare flavor-changing neutral current process
$B^{+}\rightarrow K^{+}\tau^{+}\tau^{-}$ using data from the BABAR experiment.
The data sample, collected at the center-of-mass energy of the $\Upsilon{(4S)}$
resonance, corresponds to a total integrated luminosity of 424 fb$^{-1}$ and to
471 million $B\overline{B}$ pairs. We reconstruct one $B$ meson, produced in
the $\Upsilon{(4S)}\rightarrow B^{+} B^{-}$ decay, in one of many hadronic
decay modes and search for activity compatible with a $B^{+}\rightarrow K^{+}
\tau^{+}\tau^{-}$ decay in the rest of the event. Each $\tau$ lepton is
required to decay leptonically into an electron or muon and neutrinos.
Comparing the expected number of background events with the data sample after
applying the selection criteria, we do not find evidence for a signal. The
measured branching fraction is ($1.31^{+0.66}_{-0.61}$(
stat.)$^{+0.35}_{-0.25}$( sys.)$) \times 10^{-3}$ with an upper limit, at the
90\% confidence level, of $\mathcal{B}(B^{+}\rightarrow
K^{+}\tau^{+}\tau^{-})$$< 2.25\times 10^{-3}$.
