  Corrections to Einstein's equations that become important at small curvatures
are considered. The field equations are derived using a Palatini variation in
which the connection and metric are varied independently. In contrast to the
Einstein-Hilbert variation, which yields fourth order equations, the Palatini
approach produces second order equations in the metric. The Lagrangian
$L(R)=R-\alpha^2/R$ is examined and it is shown that it leads to equations
whose solutions approach a de Sitter universe at late times. Thus, the
inclusion of 1/R curvature terms in the gravitational action offers an
alternative explanation for the cosmological acceleration.
