In a ferromagnet, an applied electric field E invariably produces an anomalous Hall current JH that flows perpendicular to the plane defined by E and M (the magnetization). For decades, the question of whether JH is dissipationless (independent of the scattering rate) has been debated without experimental resolution. In the ferromagnetic spinel CuCr2Se4-xBrx, the resistivity rho (at low temperature) may be increased by several decades by varying x (Br) without degrading M. We show that JH/E (normalized per carrier, at 5 kelvin) remains unchanged throughout. In addition to confirming the dissipationless nature of JH, our finding has implications for the generation and study of spin-Hall currents in bulk samples.