  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.
