  Motivated by recent experimental progress in high-resolution scanning
tunneling microscopy (STM) techniques, we propose to investigate the local
quasiparticle density of states around a unitary impurity in the heavy fermion
superconductor CeCoIn$_{5}$. Based on the T-matrix approach we obtain a sharp
nearly zero-energy resonance state (ZERS) in the strong impurity potential
scattering localized around the impurity, and find qualitative differences in
the spatial pattern of the tunneling conductance modulated by the nodal
structure of the superconducting gap. These unique features may be used as a
probe of the superconducting gap symmetry and in combination with the further
STM measurements, may help to confirm the $d_{x^{2}-y^{2}}$ pairing in
CeCoIn$_{5}$ at ambient pressure.
