  The chaotic inflationary model of the early universe, proposed by Linde is
explored in the brane world considering matter described by a minimally coupled
self interacting scalar field. We obtain cosmological solutions which admit
evolution of a universe either from a singularity or without a singularity. It
is found that a very weakly coupled self-interacting scalar field is necessary
for a quartic type potential in the brane world model compared to that
necessary in general relativity. In the brane world sufficient inflation may be
obtained even with an initial scalar field having value less than the Planck
scale. It is found that if the universe is kinetic energy dominated to begin
with, it transits to an inflationary stage subsequently.
