  In this paper, we study the chameleon profile in inhomogeneous density
distributions and find that the fifth force in thin shell near the surface is
weaker from what expected in homogeneous density distributions. Also, we check
the validity of quasi-static approximation for the chameleon scalar field in
the astrophysical time scales. We have investigated the rolling down behaviour
of the scalar field on its effective potential inside a one solar mass red
giant star by using MESA code. We have found that the scalar field is fast
enough to follow the minimum of the potential. This adiabatic behaviour reduces
the fifth force and extends the screened regions to lower densities where the
field has smaller mass and was expected to be unscreened. As a consequence, the
star evolution is similar to what expected from standard general relativity. In
addition, considering the stability of star, an approximate constraint on the
coupling constant $\beta$ is found.
