A late epoch cosmic acceleration may be naturally entangled with cosmic coincidence—the observation that at the onset of acceleration the vacuum energy density fraction nearly coincides with the matter density fraction. In this Letter we show that this is indeed the case with the cosmology of a Friedmann-Lamaître-Robertson-Walker (FLRW) 3-brane in a five-dimensional anti–de Sitter spacetime. We derive the four-dimensional effective action on a FLRW 3-brane, from which we obtain a mass-reduction formula, namely, , where is the effective (normalized) Planck mass, is the five-dimensional cosmological constant, and is the sum of the 3-brane tension and the matter density . Although the range of variation in is strongly constrained, the big bang nucleosynthesis bound on the time variation of the effective Newton constant is satisfied when the ratio on cosmological scales. The same bound leads to an effective equation of state close to at late epochs in accordance with astrophysical and cosmological observations.