LHCb has collected the world's largest sample of charmed hadrons. This sample is used to measure the time-integrated $C\!P$ asymmetry in the Cabibbo-suppressed decay $D^0\to K^-K^+$, $A_{C\!P}(K^-K^+)$. The direct $C\!P$ asymmetries in $D^0\to K^-K^+$ and $D^0\to \pi^-\pi^+$ decays, $a_{K^-K^+}^{d}$ and $a_{\pi^-\pi^+}^{d}$, are derived by combining $A_{C\!P}(K^-K^+)$ with the time-integrated $C\!P$ asymmetry difference, $\Delta A_{C\!P}=A_{C\!P}(K^-K^+)-A_{C\!P}(\pi^-\pi^+)$, and accounting for time-dependent effects. The result consists in the first evidence for direct $C\!P$ violation in a specific $D^0$ decay.