  We present an extension of general relativity in which an $f(R)$ term \`{a}
la Palatini is added to the usual metric Einstein-Hilbert Lagrangian.
Expressing the theory in a dynamically equivalent scalar-tensor form, we show
that it can pass the Solar System observational tests even if the scalar field
is very light or massless. Applications to cosmology and astrophysics, and some
exact solutions are discussed.
