The AMANDA neutrino telescope has recently reported the detection of high-energy neutrinos spatially and temporally coincident with the flaring of the TeV blazar 1ES 1959+650 . At present , the statistical significance of this observation can not be reliably assessed , however . In this letter , we investigate whether circumstances exist where the source can produce the flux implied by the coincident events . We show that if the TeV gamma-ray emission observed from 1ES 1959+650 or other nearby TeV blazars is the result of accelerated protons interacting with nucleons , it is reasonable that AMANDA could detect several events during a flaring period . Such rates require that the spectral index of the source be rather high ( for instance \sim 2.8 for 1ES 1959+650 ) and that the Lorentz factor of the jet be fairly small ( \Gamma \sim 1 ) .