  Recently Chakravarty {\em et al.} proposed an ordered $d$-density wave (DDW)
state as an explanation of the pseudogap phase in underdoped high-temperature
cuprates. We study the competition between the DDW and superconducting ordering
based on an effective mean-field Hamiltonian. We are mainly concerned with the
effect of the DDW ordering on the electronic state around a single nonmagnetic
impurity. We find that a single subgap resonance peak appears in the local
density of state around the impurity. In the unitary limit, the position of
this resonance peak is always located at $E_r=-\mu$ with respect to the Fermi
energy. This result is dramatically different from the case of the pure
superconducting state for which the impurity resonant energy is approximately
pinned at the Fermi level. This can be used to probe the existence of the DDW
ordering in cuprates.
