We show how the presence of a very light scalar with a cubic self-interaction
in six dimensions can stabilize the extra dimensions at radii which are
naturally exponentially large, $r \sim \ell \exp [(4\pi)^3/g^2]$, where $\ell$
is a microscopic physics scale and $g$ is the (dimensionless) cubic coupling
constant. The resulting radion mode of the metric becomes a very light degree
of freedom whose mass, $m \sim 1/(M_p r^2)$ is stable under radiative
corrections. For $1/r \sim 10^{-3}$ eV the radion is extremely light, $m \sim
10^{-33}$ eV. Its couplings cause important deviations from General Relativity
in the very early universe, but naturally evolve to phenomenologically
acceptable values at present.