  The well-known Conley's theorem states that the complement of chain recurrent
set equals the union of all connecting orbits of the flow $\phi$ on the compact
metric space $X$, i.e. $X-\mathcal{CR}(\phi)=\bigcup [B(A)-A]$, where
$\mathcal{CR}(\phi)$ denotes the chain recurrent set of $\phi$, $A$ stands for
an attractor and $B(A)$ is the basin determined by $A$. In this paper we show
that by appropriately selecting the definition of random attractor, in fact we
define a random local attractor to be the $\omega$-limit set of some random
pre-attractor surrounding it, and by considering appropriate measurability, in
fact we also consider the universal $\sigma$-algebra $\mathcal
F^u$-measurability besides $\mathcal F$-measurability, we are able to obtain
the random case of Conley's theorem.
