  We introduce a quantum double quasitriangular quasi-Hopf algebra $D(H)$
associated to any quasi-Hopf algebra $H$. The algebra structure is a cocycle
double cross product. We use categorical reconstruction methods. As an example,
we recover the quasi-Hopf algebra of Dijkgraaf, Pasquier and Roche as the
quantum double $D^\phi(G)$ associated to a finite group $G$ and group 3-cocycle
$\phi$.
