  Quantum geometry of electronic wavefunctions results in fascinating
topological phenomena. A prominent example is the intrinsic anomalous Hall
effect (AHE) in which a Hall voltage arises in the absence of an applied
magnetic field. The AHE requires a coexistence of Berry curvature and
spontaneous time-reversal symmetry breaking. These conditions can be realized
in two-dimensional moir\'e systems with broken $xy$-inversion symmetry
($C_{2z}$) that host flat electronic bands. Here, we explore helical trilayer
graphene (HTG), three graphene layers twisted sequentially by the same angle
forming two misoriented moir\'e patterns. Although HTG is globally
$C_{2z}$-symmetric, surprisingly we observe clear signatures of topological
bands. At a magic angle $\theta_\mathrm{m}\approx 1.8^\circ$, we uncover a
robust phase diagram of correlated and magnetic states using magnetotransport
measurements. Lattice relaxation leads to large periodic domains in which
$C_{2z}$ is broken on the moir\'e scale. Each domain harbors flat topological
bands with valley-contrasting Chern numbers $\pm(1,-2)$. We find correlated
states at integer electron fillings per moir\'e unit cell $\nu=1,2,3$ and
fractional fillings $2/3,7/2$ with the AHE arising at $\nu=1,3$ and $2/3,7/2$.
At $\nu=1$, a time-reversal symmetric phase appears beyond a critical electric
displacement field, indicating a topological phase transition. Finally,
hysteresis upon sweeping $\nu$ points to first-order phase transitions across a
spatial mosaic of Chern domains separated by a network of topological gapless
edge states. We establish HTG as an important platform that realizes ideal
conditions for exploring strongly interacting topological phases and, due to
its emergent moir\'e-scale symmetries, demonstrates a novel way to engineer
topology.
