  In the model of Chain Inflation, a sequential chain of coupled scalar fields
drives inflation. We consider a multidimensional potential with a large number
of bowls, or local minima, separated by energy barriers: inflation takes place
as the system tunnels from the highest energy bowl to another bowl of lower
energy, and so on until it reaches the zero energy ground state. Such a
scenario can be motivated by the many vacua in the stringy landscape, and our
model can apply to other multidimensional potentials. The ''graceful exit''
problem of Old Inflation is resolved since reheating is easily achieved at each
stage. Coupling between the fields is crucial to the scenario. The model is
quite generic and succeeds for natural couplings and parameters. Chain
inflation succeeds for a wide variety of energy scales -- for potentials
ranging from 10MeV scale inflation to $10^{16}$ GeV scale inflation.
