  We quantise a Poisson structure on H^{n+2g}, where H is a semidirect product
group of the form $G\ltimes\mathfrak{g}^*$. This Poisson structure arises in
the combinatorial description of the phase space of Chern-Simons theory with
gauge group $G\ltimes\mathfrak{g}^*$ on $R \times S_{g,n}$, where S_{g,n} is a
surface of genus g with n punctures. The quantisation of this Poisson structure
is a key step in the quantisation of Chern-Simons theory with gauge group
$G\ltimes\mathfrak{g}^*$. We construct the quantum algebra and its irreducible
representations and show that the quantum double D(G) of the group G arises
naturally as a symmetry of the quantum algebra.
