  We have investigated the Brans-Dicke Chameleon theory of gravity and obtained
exact solutions of the scale factor $a(t)$, scalar field $\phi(t)$, an
arbitrary function $f(\phi)$ which interact with the matter Lagrangian in the
action of the Brans-Dicke Chameleon theory and potential $V(\phi)$ for
different epochs of the cosmic evolution. We plot the functions $a(t)$,
$\phi(t)$, $f(t)$ and $V(\phi)$ for different values of the Brans-Dicke
parameter. In our models, there is no accelerating solution, only decelerating
one with $q>0$. The physical cosmological distances have been investigated
carefully. Further the statefinder parameters pair and deceleration parameter
are discussed.
