  Let $\phi$ be a rank $r$ Drinfeld $\BF_q[T]$-module determined by $\phi_T(X)
= TX+g_1X^q+...+g_{r-1}X^{q^{r-1}}+X^{q^r}$, where $g_1,...,g_{r-1}$ are
algebraically independent over $\BF_q(T)$. Let $N\in\BF_q[T]$ be a polynomial,
and $k/\BF_q$ an algebraic extension. We show that the Galois group of
$\phi_N(X)$ over $k(T,g_1,...,g_{r-1})$ is isomorphic to
$\GL_r(\BF_q[T]/N\BF_q[T])$, settling a conjecture of Abhyankar.
