  We present the first measurement of the CP violating charge asymmetry in
$B^\pm \to \mu^\pm \nu_\mu {D}^0$ decays using the full Run II integrated
luminosity of 10.4 fb$^{-1}$ in proton-antiproton collisions collected with the
D0 detector at the Fermilab Tevatron Collider. We measure a difference in the
yield of $B^-$ and $B^+$ mesons in these decays by fitting the reconstructed
invariant mass distributions. This results in an asymmetry of $A^{\mu D^{0}}
=\left[ -0.14 \pm 0.20 \right]\%$, which is consistent with standard model
predictions.
