Typically, Martian volcanoes show either a total absence of crustal magnetism or a local magnetic mimimum. Hadriaca Patera is the only volcano on Mars with a clear positive magnetic anomaly directly over the volcanic edifice, as determined by electron reflection magnetometry. Hadriaca's topography, lava flow crater ages, gravity anomaly, position relative to the Hellas rim and past aqueous environment provide geological constraints on possible scenarios to explain this unusual magnetic signature. The two most probable scenarios are a) pre-Hellas thermoremanent magnetization (TRM) of a deep-seated magma body followed by post-Hellas intrusive partial thermal demagnetization and b) post-Hellas emplacement of the volcano and TRM in a global magnetic field. It is thus likely that Mars had at least one of the following: highland volcanism in pre-Hellas times (older than any datable volcanic feature on the planet) or an active dynamo some time after the Hellas impact.