We report the first measurement of a ratio lambda(beta(b))/lambda(beta(c)) of bound-state ((lambda(beta(b))) and continuum-state (lambda(beta(c))) beta(-)-decay rates for the case of bare 207Tl81+ ions. These ions were produced at the GSI fragment separator FRS by projectile fragmentation of a 208Pb beam. After in-flight separation with the Brho-deltaE-Brho method, they were injected into the experimental storage-ring ESR at an energy of 400.5A MeV, stored, and electron cooled. The number of both the 207Tl81+ ions and their bound-state beta(-)-decay daughters, hydrogen-like 207Pb81+ ions, were measured as a function of storage time by recording their Schottky-noise intensities. The experimental result, lambda(beta(b))/lambda(beta(c)) = 0.188(18), is in very good agreement with the value of 0.171(1) obtained from theory employing spectra of allowed transitions.