In this, the first of a series of papers on quantum field theory in de Sitter spacetime, the invariant vacuum state appropriate for inflationary models of the early universe is identified and shown to decay due to the Hawking effect. The created pairs have an energy-momentum which leads to a first-order decrease of the effective cosmological constant, independently of any matter phase transition. A mechanism for dynamically relaxing ..lambda../sub eff/..-->..0 is thereby suggested.