  SrRuO$_3$ heterostructures grown in the (111) direction are a rare example of
thin film ferromagnets. By means of density functional theory plus dynamical
mean field theory we show that the half-metallic ferromagnetic state with an
ordered magnetic moment of 2$\mu_{B}$/Ru survives the ultimate dimensional
confinement down to a bilayer, even at elevated temperatures of 500$\,$K. In
the minority channel, the spin-orbit coupling opens a gap at the linear band
crossing corresponding to $\frac34$ filling of the $t_{2g}$ shell. We
demonstrate that the respective state is Haldane's quantum anomalous Hall state
with Chern number $C$=1, without an external magnetic field or magnetic
impurities.
