We show that the breakdown of time-reversal invariance, confirmed by the recent polar Kerr effect measurements in the cuprates, implies the existence of an anomalous Nernst effect in the pseudogap phase of underdoped cuprate superconductors. Modeling the time-reversal-breaking ordered state by the chiral d-density-wave state, we find that the magnitude of the Nernst effect can be sizable even at temperatures much higher than the superconducting transition temperature. These results imply that the experimentally found Nernst effect at the pseudogap temperatures may be due to the chiral d-density wave ordered state with broken time-reversal invariance.
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