  We have performed an exclusive measurement of the $K^{-}+\! ~^{3}{\rm He} \to
\Lambda pn$ reaction at an incident kaon momentum of $1\ {\rm GeV}/c$.In the
$\Lambda p$ invariant mass spectrum, a clear peak was observed below the mass
threshold of $\bar{K}\!+\!N\!+\!N$, as a signal of the kaonic nuclear bound
state, $\bar{K}NN$.The binding energy, decay width, and $S$-wave Gaussian
reaction form-factor of this state were observed to be $B_{K} = 42\pm3({\rm
stat.})^{+3}_{-4}({\rm syst.})\ {\rm MeV}$, $\Gamma_{K} = 100\pm7({\rm
stat.})^{+19}_{-9}({\rm syst.})\ {\rm MeV}$, and $Q_{K} = 383\pm11({\rm
stat.})^{+4}_{-1}({\rm syst.})\ {\rm MeV}/c$, respectively. The total
production cross-section of $\bar{K}NN$, determined by its $\Lambda p$ decay
mode, was $\sigma^{tot}_{K} \cdot BR_{\Lambda p} = 9.3\pm0.8({\rm
stat.})^{+1.4}_{-1.0}({\rm syst.})\ \mu{\rm b}$.We estimated the branching
ratio of the $\bar{K}NN$ state to the $\Lambda p$ and $\Sigma^{0}p$ decay modes
as $BR_{\Lambda p}/BR_{\Sigma^{0}p} \sim 1.7$, by assuming that the physical
processes leading to the $\Sigma N\!N$ final states are analogous to those of
$\Lambda pn$.
