We report an indication that the elastic scattering rate of solar B8 neutrinos with electrons in the Super-Kamiokande detector is larger when the neutrinos pass through Earth during nighttime. We determine the day-night asymmetry, defined as the difference of the average day rate and average night rate divided by the average of those two rates, to be [-3.2 ± 1.1(stat) ± 0.5(syst)]%, which deviates from zero by 2.7 σ. Since the elastic scattering process is mostly sensitive to electron-flavored solar neutrinos, a nonzero day-night asymmetry implies that the flavor oscillations of solar neutrinos are affected by the presence of matter within the neutrinos' flight path. Super-Kamiokande's day-night asymmetry is consistent with neutrino oscillations for 4 × 10(-5) eV(2) ≤ Δm 2(21) ≤ 7 × 10(-5) eV(2) and large mixing values of θ12, at the 68% C.L.