  We report a measurement of the time-dependent ratio of $D^0\to K^+\pi^-$ to
$D^0\to K^-\pi^+$ decay rates in $D^{*+}$-tagged events using 1.0\,fb$^{-1}$ of
integrated luminosity recorded by the LHCb experiment. We measure the mixing
parameters $x'^2=(-0.9\pm1.3)\times10^{-4}$, $y'=(7.2\pm2.4)\times10^{-3}$ and
the ratio of doubly-Cabibbo-suppressed to Cabibbo-favored decay rates
$R_D=(3.52\pm0.15)\times10^{-3}$. The result excludes the no-mixing hypothesis
with a probability corresponding to 9.1 standard deviations and represents the
first observation of charm mixing from a single measurement
