The recently proposed inflationary Universe scenario1-4 explains several of the mysteries of modern cosmology. I argue here that it also provides a natural explanation for the origin of time asymmetry ('time's arrow') in the Universe. The new feature which inflation injects into this long-standing problem is the temporary dominance of the cosmological term in the gravitational field equations, which acts as a sort of repulsive gravity. This term generates huge quantities of energy and radiation (or matter) entropy, while drastically reducing the entropy density of the gravitational field. It thus establishes a large gap between the radiation entropy and the gravitational entropy, which gravity is now trying to close.
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