  We report the observation of a quantum anomalous Hall effect in twisted
bilayer graphene showing Hall resistance quantized to within .1\% of the von
Klitzing constant $h/e^2$ at zero magnetic field.The effect is driven by
intrinsic strong correlations, which polarize the electron system into a single
spin and valley resolved moir\'e miniband with Chern number $C=1$. In contrast
to extrinsic, magnetically doped systems, the measured transport energy gap
$\Delta/k_B\approx 27$~K is larger than the Curie temperature for magnetic
ordering $T_C\approx 9$~K, and Hall quantization persists to temperatures of
several Kelvin. Remarkably, we find that electrical currents as small as 1~nA
can be used to controllably switch the magnetic order between states of
opposite polarization, forming an electrically rewritable magnetic memory.
