Self-propagating exothermic chemical reactions can generate electrical pulses when guided along a conductive conduit such as a carbon nanotube. However, these thermopower waves are not described by an existing theory to explain the origin of power generation or why its magnitude exceeds the predictions of the Seebeck effect. In this work, we present a quantitative theory that describes the electrical dynamics of thermopower waves, showing that they produce an excess thermopower additive to the Seebeck prediction. Using synchronized, high-speed thermal, voltage, and wave velocity measurements, we link the additional power to the chemical potential gradient created by chemical reaction (up to 100 mV for picramide and sodium azide on carbon nanotubes). This theory accounts for the waves' unipolar voltage, their ability to propagate on good thermal conductors, and their high power, which is up to 120% larger than conventional thermopower from a fiber of all-semiconducting SWNTs. These results underscore the potential to exceed conventional figures of merit for thermoelectricity and allow us to bound the maximum power and efficiency attainable for such systems.