  We show that Supersymmetric effects driven by penguin contributions to the $b
\to c \tau \nu_\tau$ transition are able to account simultaneously for a
sizeable increase of both branching ratios of $\bar{B}\to D
\tau\bar{\nu}_{\tau}$ and $\bar{B} \to D^{*} \tau\bar{\nu}_{\tau}$ with respect
to the Standard Model predictions, thereby approaching their experimentally
measured values. We emphasise that a light chargino and neutralino, with masses
less 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 theoretical
predictions with respect to current data.
