Can a single atom coherently excited by on-resonance laser radiation generate a random telegraph signal with frequent periods of darkness in the fluorescence radiation, reflecting the quantum jumps of the atomic transitions? Erber and Putterman1 have proposed that such a random telegraph, predicted earlier2 for incoherent excitation, persists when the excitation is coherent and resonant with the unperturbed atomic transition frequencies. They argue that such an atomic telegraph is cryptographically equivalent to an infinite computer in its ability to generate random numbers, and would provide new tests of basic quantum theory. Here we argue that any periods of darkness in the light emitted by a coherently driven atom excited on resonance must be exceedingly rare.