Annual modulation of rays from () reactions in the Soudan Underground Laboratory was observed using a 12-liter scintillation detector. This significant annual modulation, measured over 4 years, can mimic the signature for dark matter and can also generate potential background events for neutrinoless double- decay experiments. The measured annual modulation of the event rate from () reactions is strongly correlated with the time-varying radon concentration observed independently in the laboratory. The flux from radon decay is simulated starting from the measured radon concentration, and the -ray flux is determined using the convolution of the flux and the cross sections for () reactions. The calculated -ray flux is sufficient to generate the measured event rate that exhibits an annual modulation.