We present a reconstruction technique for models of f (R) gravity from the Chaplygin scalar field in flat de Sitter spacetimes. Exploiting the equivalence between f (R) gravity and scalar-tensor theories, and treating the Chaplygin gas as a scalar field model in a universe without conventional matter forms, the Lagrangian densities for the f (R) action are derived. Exact f (R) models and corresponding scalar field potentials are obtained for asymptotically de Sitter spacetimes in early and late cosmological expansion histories. It is shown that the reconstructed f (R) models all have General Relativity as a limiting solution.