  We construct a unique G-equivariant graded star product on the algebra
$S(g)/I$ of polynomial functions on the minimal nilpotent coadjoint orbit
$\Omin$ of G where G is a complex simple Lie group and $g\neq\sl_2(C)$. This
strengthens the result of Arnal, Benamor, and Cahen.
  Our main result is to compute, for G classical, the star product of a
momentum function $\mu_x$ with any function f. We find $\mu_x\star
f=\mu_xf+\half\{\mu_x,f\}t+\Lambda^x(f)t^2$. For $\g$ different from
$sp_n(\C)$, $\Lambda^x$ is not a differential operator. Instead $\Lamda^x$ is
the left quotient of an explicit order 4 algebraic differential operator $D^x$
by an order 2 invertible diagonalizable operator. Precisely,
$\Lambda^x=-{1/4}\frac{1}{E'(E'+1)}D^x$ where $E'$ is a positive shift of the
Euler vector field. Thus $\mu_x\star f$ is not local in f.
  Using $\star$ we construct a positive definite hermitian inner product on
$Sg/I$. The Hilbert space completion of $Sg/I$ is then a unitary representation
of $G$. This quantizes $\Omin$ in the sense of geometric quantization and the
orbit method.
