In the presence of a magnetic field, electronic states of moiré quantum materials develop a Hofstadter spectrum that provides a distinctive setting for studying the interplay between band topology and strong electron-electron interaction. Using scanning tunneling microscopy, we studied Hofstadter’s states in bilayer graphene aligned with hexagonal boron nitride and directly visualized the formation of interaction-driven symmetry breaking Chern insulators. Our measurements revealed the formation of phases that double, triple, or quadruple the moiré unit cell at fractional filling of the Hofstadter bands as well as states with complex intra–unit cell wave functions. We visualized two distinct quantum phenomena in different Chern states, including quantum melting driven by the appearance and proliferation of topological defects and a quantum transition co-occurring with phase competition and separation.