Au/Si(111) surface superstructures exhibit a two-dimensional glass-crystal transition between the β-√3×√3 (glass) and the 6×6 (crystal) phases, in a monatomic layer just by controlling thermal treatment. We have performed electrical resistance measurements at this transition by a microscopic 4-point probe method at various temperatures ranging from room temperature to 120 K, and succeeded in detecting a clear difference in resistance between the two phases. The 6×6 phase has a lower resistance than the β-√3×√3 phase at all temperatures. The resistance of each phase decrease with temperature increase, showing a semiconducting character. By comparing with photoemission spectroscopy data, the electrical conduction mechanism in high temperature region (above ∼175 K) is band conduction of thermally excited electrons with an activation energy ΔE∼100 meV for both phases. The mechanism for low temperature region (below ∼175 K) is hopping conduction with an activation energy ΔE∼3 meV and 8 meV for the 6×6 and the β-√3×√3 phases, respectively. The widths of localization areas are consistent with STM images.