We present observations of a giant Lyα blob (LAB) in the SSA22 protocluster at z = 3.1, SSA22-LAB1, taken with the Atacama Large Millimeter/submillimeter Array. Dust continuum, along with [C ii] 158 μm and CO(4–3) line emission have been detected in LAB1, showing complex morphology and kinematics across a ∼100 kpc central region. Seven galaxies at z = 3.0987–3.1016 in the surroundings are identified in [C ii] and dust continuum emission, with two of them potential companions or tidal structures associated with the most massive galaxies. Spatially resolved [C ii] and infrared luminosity ratios for the widely distributed media (L[Cɪɪ]/LIR ≈ 10−2−10−3) suggest that the observed extended interstellar media are likely to have originated from star formation activity and the contribution from shocked gas is probably not dominant. LAB1 is found to harbor a total molecular gas mass Mmol = (8.7 ± 2.0) × 1010 M⊙, concentrated in the core region of the Lyα-emitting area. While (primarily obscured) star formation activity in the LAB1 core is one of the most plausible power sources for the Lyα emission, multiple major mergers found in the core may also play a role in making LAB1 exceptionally bright and extended in Lyα as a result of cooling radiation induced by gravitational interactions.