We study the electronic structure near impurities in the d-density-wave (DDW) state, a possible candidate phase for the pseudogap region of the high-temperature superconductors. We show that the density of states near a nonmagnetic impurity in the DDW state is qualitatively different from that in a superconductor with dx(2)(-y(2)) symmetry. Thus, the electronic structure near impurities can provide insight into the nature of the two phases recently observed by scanning tunneling microscopy experiments in the superconducting state of underdoped Bi-2212 compounds.