In an emulsion-counter hybrid experiment performed at J-PARC, a $Xi^-$ absorption event was observed which decayed into twin single-$Lambda$ hypernuclei. Kinematic calculations enabled a unique identification of the reaction process as $Xi^{-} + ^{14}$N$ rightarrow ^{10}_Lambda$Be + $^5_Lambda$He. For the binding energy of the $Xi^{-}$ hyperon in the $Xi^-$-$^{14}$N system a value of $1.27 pm 0.21$ MeV was deduced. The energy level of $Xi^-$ is likely a nuclear $1p$ state which indicates a weak ${Xi}N$-$LambdaLambda$ coupling.
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