  Let $(f_n)_{n=1}^\infty$ be a sequence of nonlinear polynomials satisfying
some mild conditions. Furthermore, let $F_m(z)=(f_m\circ f_{m-1}\ldots \circ
f_1)(z)$ and $\rho_m$ be the leading coefficient for $F_m$. It is shown that on
the Julia set $J_{(f_n)}$, the Chebyshev polynomial of the degree deg${F_m}$ is
of the form $F_m(z)/\rho_m-\tau_m$ for all $m\in\mathbb{N}$ where
$\tau_m\in\mathbb{C}$. This generalizes the result obtained for autonomous
Julia sets.
