  In inflationary scenarios with more than one scalar field, inflation may
proceed even if each of the individual fields has a potential too steep for
that field to sustain inflation on its own. We show that scalar fields with
exponential potentials evolve so as to act cooperatively to assist inflation,
by finding solutions in which the energy densities of the different scalar
fields evolve in fixed proportion. Such scaling solutions exist for an
arbitrary number of scalar fields, with different slopes for the exponential
potentials, and we show that these solutions are the unique late-time
attractors for the evolution. We determine the density perturbation spectrum
produced by such a period of inflation, and show that with multiple scalar
fields the spectrum is closer to the scale-invariant than the spectrum that any
of the fields would generate individually.
