  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.
