When two sheets of graphene are stacked at a small twist angle, the resulting flat superlattice minibands are expected to strongly enhance electron-electron interactions. Here, we present evidence that near three-quarters (34/34) filling of the conduction miniband, these enhanced interactions drive the twisted bilayer graphene into a ferromagnetic state. In a narrow density range around an apparent insulating state at 34/34, we observe emergent ferromagnetic hysteresis, with a giant anomalous Hall (AH) effect as large as 10.4 kilohms and indications of chiral edge states. Notably, the magnetization of the sample can be reversed by applying a small direct current. Although the AH resistance is not quantized, and dissipation is present, our measurements suggest that the system may be an incipient Chern insulator.