We report the result from observations conducted with the Atacama Large Millimeter/submillimeter Array (ALMA) to detect [C II] 158 \ensuremathμm fine structure line emission from galaxies embedded in one of the most spectacular Ly\ensuremathα blobs (LABs) at z = 3.1, SSA22-LAB1. Of three dusty star-forming galaxies previously discovered by ALMA 860 \ensuremathμm dust continuum survey toward SSA22-LAB1, we detected the [C II] line from one, LAB1-ALMA3 at z = 3.0993 \ensuremath± 0.0004. No line emission was detected, associated with the other ALMA continuum sources or from three rest-frame UV/optical selected z$_spec$ ≃ 3.1 galaxies within the field of view. For LAB1-ALMA3, we find relatively bright [C II] emission compared to the infrared luminosity (L$_[C II]$/L$_IR$ \ensuremath≈ 0.01) and an extremely high [C II] 158 \ensuremathμm and [N II] 205 \ensuremathμm 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\ensuremathα emission and interstellar medium conditions of associated galaxies is yet to be understand.