Moiré semiconductors built on angle-aligned transition metal dichalcogenide (TMD) heterobilayers provide a physical realization of the Kondo lattice model, in which one TMD layer is prepared in a Mott insulating state supporting a lattice of local magnetic moments and the other layer in a metallic state supporting itinerant carriers. The artificial Kondo lattice enables the exploration of exotic states of matter near a continuously tunable Kondo breakdown. Here we report the emergence of a symmetry-broken Chern insulator at a moiré hole filling factor 4/3 in angle-aligned MoTe2/WSe2 moiré bilayers, which realize a chiral Kondo lattice. The symmetry-broken Chern insulator, which exhibits integer quantized Hall conductance at a fractional moiré filling, breaks the translational symmetry of the lattice spontaneously; it also appears only near a magnetic field-induced Kondo breakdown in the mixed-valence regime of the material. We further demonstrate that the magnetic field required to induce the Kondo breakdown and to stabilize the symmetry-broken Chern insulator is twist angle dependent. The results present new opportunities for exploring the subtle interplay between topology and Kondo interactions in moiré semiconductors.