The thermopower and resistivity of bulk superconducting HgBa2Ca2Cu3O8+δ (Hg-1223) have been measured for 15 samples (prepared from two batches) subjected to various annealing treatments in oxygen or nitrogen; all but two samples had values of zero-resistance Tc of approximately 134 K. In the normal state, the thermopower of the annealed samples shows a similar shape as a function of temperature: it decreases as temperature increases, with the rate of decrease slowing down at higher temperatures. The thermopower remains positive up to room temperature in all of our samples despite the high Tc values and annealing in oxygen, suggesting that the samples remain slightly underdoped. © 1995 The American Physical Society.