We present the first results of the Chandra and optical follow-up observations of hard X-ray sources detected in the ASCA Medium Sensitivity Survey (AMSS). Optical identifications are made for five objects. Three of them show either weak or absent optical narrow emission lines and are at low redshift <z>~0.06. One of them is a broad line object at z=0.910 and one is a z=0.460 object with only narrow lines. All the narrow line objects show strong evidence for absorption in their X-ray spectra. Their line ratios are consistent with a Seyfert II/LINER identification as are the line widths. The three low redshift objects have the colors of normal galaxies and apparently the light is dominated by stars. This could be due to the extinction of the underlying nuclear continuum by the same matter that absorbs X-rays and/or due to the dilution of the central source by starlight. These results suggest that X-ray sources that appear as ``normal galaxies in optical and near-IR bands significantly contribute to the hard X-ray background. This population of objects has a high space density and probably dominates the entire population of active galaxies.