  We determine an upper bound for a possible right-handed $b{\to}c$ quark
current admixture in semileptonic $\bar{B} \to X_{c} \ell^{-} \bar{\nu}$ decays
from a simulateous fit to moments of the lepton-enery and hadronic-mass
distribution measured as a function of the lower limit on the lepton energy,
using data measured by the \babar\ detector. The right-handed admixture is
parametrized by a new parameter $c_R$ as coefficient of computed moments with
right-handed quark current. For the standard model part we use the prediction
of the heavy-quark expansion (HQE) up to order $1/m_b^3$ and perturbative
corrections and for the right-handed contribution only up to order $1/m_b^2$
and perturbative corrections. We find $\cR=0.05\asympm{+0.33}{-0.50}$ in
agreement with the standard-model prediction of zero. Additionally, we give a
contraint on a possible right-handed admixture from exclusive decays, which is
with a value of $\cR =0.01{\pm}0.03$ more restrictive than our value from the
inclusive fit. The difference in \Vcb between the inclusive and exclusive
extraction is only slightly reduced when allowing for a right-handed admixture
in the range of $\cR=0.01 {\pm} 0.03$.
