Crustal magnetization of rocks in regions of Mars surface testifies to an era of dynamo activity. I examine the possibility that the dynamo that operated then, in the first 400-600 Ma after Mars formed, was powered by a crystallizing subsurface magma ocean. Of the ways that a magma ocean dynamo could operate, on Mars only turbulent and magnetostrophic dynamos seem feasible; geostrophic dynamos do not seem so unless very high heat flows, 100-1000 times present, are invoked. Given the anticipated information from the future InSight lander mission, it will be difficult to assess where the dynamo originated unless an inner core is discovered, rendering the dynamo likely to have operated in the core.