  Let $F$ be a local non-Archimedean field with ring of integers $o$. Let $\bf
X$ be a one-dimensional formal $o$-module of $F$-height $n$ over the algebraic
closure of the residue field of $o$. By the work of Drinfeld, the universal
deformation $X$ of $\bf X$ is a formal group over a power series ring $R_0$ in
$n-1$ variables over the completion of the maximal unramified extension of $o$.
For $h \in \{0,...,n-1\}$ let $U_h$ be the subscheme of $\Spec(R_0)$ where the
connected part of the associated divisible module of $X$ has height $h$. Using
the theory of Drinfeld level structures we show that the representation of the
fundamental group of $U_h$ on the Tate module of the etale quotient is
surjective.
