  We measure the charge asymmetry $A\equiv(N^{++} - N^{--})/(N^{++} + N^{--})$
of like-sign dimuon events in 6.1~fb$^{-1}$ of $p\bar{p}$ collisions recorded
with the D0 detector at a center-of-mass energy $\sqrt{s}=1.96$~TeV at the
Fermilab Tevatron collider. From $A$ we extract the like-sign dimuon charge
asymmetry in semileptonic $b$-hadron decays:
$\aslb=-0.00957\pm0.00251\thinspace({\rm stat})\pm0.00146\thinspace({\rm
sys})$. It differs by 3.2~standard deviations from the standard model
prediction $\aslb({\rm SM})=(-2.3^{+0.5}_{-0.6})\times10^{-4}$, and provides
first evidence of anomalous $CP$ violation in the mixing of neutral $B$ mesons.
