We have identified the candidates for the primordial galaxies in the process of formation in the Hubble Deep Field (hereafter HDF). In order to select these objects we have removed objects brighter than 29-th magnitude in the HDF images and smoothed the maps with the Gaussian filters with the FWHM of 0.8' and 4' to obtain the difference maps. This has enabled us to find. very faint diffuse structures close to the sky level. Peaks are identified in the difference map for each of three HDF chips with three filters (F450W, F606W, and F814W). They have the apparent AB magnitudes typically between 29 and 31. The objects identified in different wavelengths filters have a strong cross-correlations. The correlation lengths are about 0.8'. This means that an object found in one filter can be also found as a peak within 0.8' separation in another filter, thus telling the reality of the identified objects. This angular scale is also the size of the primordial galaxies which have strong color fluctuations on their surfaces. Their large-scale distribution quite resembles that of nearby galaxies, supporting the idea that these objects are ancestors of the present bright galaxies forming at statistically high density regions. Inspections on individual objects show that these primordial galaxy candidates have tiny multiple glares embedded in diffuse backgrounds. Their radial light distributions are quite different from that of nearby bright galaxies. We may be now looking at the epoch of galaxy formation.