  We consider slow-roll inflation in the context of recently proposed
four-dimensional effective gravity induced on the world-volume of a three-brane
in five-dimensional Einstein gravity. We find significant modifications of the
simplest chaotic inflationary scenario when the five-dimensional Planck scale
is below about 10^{17} GeV. We use the comoving curvature perturbation, which
remains constant on super-Hubble scales, in order to calculate the spectrum of
adiabatic density perturbations generated. Modifications to the Friedmann
constraint equation lead to a faster Hubble expansion at high energies and a
more strongly damped evolution of the scalar field. This assists slow-roll,
enhances the amount of inflation obtained in any given model, and drives the
perturbations towards an exactly scale-invariant Harrison-Zel'dovich spectrum.
In chaotic inflation driven by a massive scalar field we show that inflation
can occur at field values far below the four-dimensional Planck scale, though
above the five-dimensional fundamental scale.
