We performed high-resolution scanning tunneling microscopy/spectroscopy on an optimally-doped Ca2-xNaxCuO2Cl2 crystal with Tc ∼ 25 K. The so-called "checkerboard" local-density-of-state modulation previously found in heavily underdoped regime also manifests in the spectroscopic map of the optimally-doped sample. In addition, spatially-inhomogeneous energy gap with peaks at the gap edges is observed below about 10 meV. The gap tends to be buried at elevated temperatures and correlates with the checkerboard modulation. These results suggest that the gap is related to superconductivity which coexists with the checkerboard modulation. © 2007 Elsevier B.V. All rights reserved.