We report the result from observations conducted with the Atacama Large Millimeter/submillimeter Array (ALMA) to detect [C II] 158 mu m fine structure line emission from galaxies embedded in one of the most spectacular Ly alpha blobs (LABs) at z = 3.1, SSA22-LAB1. Of three dusty star-forming galaxies previously discovered by ALMA 860 mu m dust continuum survey toward SSA22-LAB1, we detected the [C II] line from one, LAB1-ALMA3 at z = 3.0993 +/- 0.0004. No line emission was detected, associated with the other ALMA continuum sources or from three rest-frame UV/optical selected z(spec) similar or equal to 3.1 galaxies within the field of view. For LAB1-ALMA3, we find relatively bright [C II] emission compared to the infrared luminosity (L-[C II]/LIR approximate to 0.01) and an extremely high [C II] 158 mu m and [N II] 205 mu m emission line ratio (L[C II]/L[N II] > 55). The relatively strong [C II] emission may be caused by abundant photodissociation regions and sub-solar metallicity, or by shock heating. The origin of the unusually strong [C II] emission could be causally related to the location within the giant LAB, although the relationship between extended Ly alpha emission and interstellar medium conditions of associated galaxies is yet to be understand.