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We present the first measurements of branching fractions of rare tau-leptondecays, $\tau^- \rightarrow \pi^- \nu_{\tau} \ell^+ \ell^-$ ($\ell = e$ or$\mu$), using a data sample corresponding to 562 fb$^{-1}$ collected at acenter-of-mass energy of 10.58 GeV with the Belle detector at the KEKBasymmetric-energy $e^+ e^-$ collider. The $\tau^- \rightarrow \pi^- \nu_\taue^+ e^-$ decay is observed for the first time with 7.0$\sigma$ significance.The partial branching fraction determined by the structure-dependent mechanismsmediated by either a vector or an axial-vector current for the mass region$M_{\pi e e}>1.05$ GeV/$c^2$ is measured to be $\mathcal{B}(\tau^-\rightarrow\pi^- \nu_\tau e^+ e^-)[M_{\pi^- e^+ e^-}>1.05~{\rm GeV}/c^2] = (5.90 \pm 0.53\pm 0.85 \pm 0.11) \times 10^{-6}$, where the first uncertainty is statistical,the second is systematic, and the third is due to the model dependence. In thefull phase space, due to the different detection efficiencies for thestructure-dependent mechanisms mediated by axial-vector and vector currents,the branching fraction varies from $\mathcal{B}_{A}(\tau^-\rightarrow \pi^-\nu_\tau e^+ e^-) = (1.46 \pm 0.13 \pm 0.21) \times 10^{-5}$ to$\mathcal{B}_{V}(\tau^-\rightarrow \pi^- \nu_\tau e^+ e^-) = (3.01 \pm 0.27 \pm0.43) \times 10^{-5}$, respectively. An upper limit is set on the branchingfraction of the $\tau^- \rightarrow \pi^- \nu_\tau \mu^+ \mu^-$ decay,$\mathcal{B}(\tau^-\rightarrow \pi^- \nu_\tau \mu^+ \mu^-) < 1.14 \times10^{-5}$, at the 90% confidence level.

Observation of $ \tau^- \rightarrow \pi^- \nu_{\tau} e^+ e^-$ and search for $\tau^- \rightarrow \pi^- \nu_{\tau} \mu^+ \mu^-$