  We examine the late-time (nucleosynthesis and later) cosmological
implications of brane-world scenarios having large (millimeter sized) extra
dimensions. In particular, recent proposals for understanding why the extra
dimensions are so large in these models indicate that moduli like the radion
appear (to four-dimensional observers) to be extremely light, with a mass of
order 10^{-33} eV, allowing them to play the role of the light scalar of
quintessence models. The radion-as-quintessence solves a long-standing problem
since its small mass is technically natural, in that it is stable against
radiative corrections. Its challenges are to explain why such a light particle
has not been seen in precision tests of gravity, and why Newton's constant has
not appreciably evolved since nucleosynthesis. We find the couplings suggested
by stabilization models can provide explanations for both of these questions.
We identify the features which must be required of any earlier epochs of
cosmology in order for these explanations to hold.
