  The $CP$ asymmetry in $B^-\to D_s^-D^0$ and $B^-\to D^-D^0$ decays is
measured using LHCb data corresponding to an integrated luminosity of 3.0
fb$^{-1}$, collected in $pp$ collisions at centre-of-mass energies of 7 and 8
TeV. The results are $A^{CP}(B^-\to D_s^-D^0)=(-0.4\pm 0.5\pm 0.5)\%$ and
$A^{CP}(B^-\to D^-D^0)=( 2.3\pm 2.7\pm 0.4)\%$, where the first uncertainties
are statistical and the second systematic. This is the first measurement of
$A^{CP}(B^-\to D_s^-D^0)$ and the most precise determination of $A^{CP}(B^-\to
D^-D^0)$. Neither result shows evidence of $CP$ violation.
