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We show that Supersymmetric effects driven by penguin contributions to the $b\to c \tau \nu_\tau$ transition are able to account simultaneously for asizeable increase of both branching ratios of $\bar{B}\to D\tau\bar{\nu}_{\tau}$ and $\bar{B} \to D^{*} \tau\bar{\nu}_{\tau}$ with respectto the Standard Model predictions, thereby approaching their experimentallymeasured values. We emphasise that a light chargino and neutralino, with massesless than 300 GeV, in addition to a large stau/snueutrino mass and a large$\tan\beta$, are essential for enhancing the effect of the lepton penguin $\tau\nu_\tau W^{\pm}$, which is responsible for the improved theoreticalpredictions with respect to current data.

Alleviating the $\bar B \to D \tau \nu$ and $\bar B \to D^* \tau \nu_\tau$ puzzle in the MSSM