  A chaotic model of the early universe within the framework of the
singularity-free solutions of Einstein's equation is suggested. The evolution
of our universe at its early stage, starting out as a small domain of the
parent universe, is governed by the dynamics of a classical scalar field $\phi$
. If in any such domain, larger than Planck length,$\dot \phi$ happens to be
very large,$\phi$ may develop a dominant inhomogeneous mode,leading to an
anisotropic inflation of the universe. The particle $\phi$ is coupled to other
particles, which are produced copiously after inflation and these thermalize
leading to a rather low temperature universe $(T \geq 10^{4} $ Gev). The
electroweak B+L Baryogenesis is assumed to account for the observed baryon
asymmetry. The universe now passes through a radiation-dominated phase, leading
eventually to a matter-dominated universe, which is isotropic and homogeneous.
The model does not depend on the details of Planck scale physics.
