We report a measurement of the top-quark mass, Mt, in the dilepton decay channel of tt→bℓ'+νℓ′b¯ℓ−ν¯ℓ using an integrated luminosity of 1.0  fb−1 of pp collisions collected with the CDF II detector. We apply a method that convolutes a leading-order matrix element with detector resolution functions to form event-by-event likelihoods; we have enhanced the leading-order description to describe the effects of initial-state radiation. The joint likelihood is the product of the likelihoods from 78 candidate events in this sample, which yields a measurement of Mt=164.5±3.9(stat.)±3.9(syst.)  GeV/c2, the most precise measurement of Mt in the dilepton channel.