  In this paper we give an explicit expression for a star product on the super
Minkowski space written in the supertwistor formalism. The big cell of the
super Grassmannian Gr(2|0, 4|1) is identified with the chiral, super Minkowki
space. The super Grassmannian is an homogeneous space under the action of the
complexification SL(4|1) of SU(2,2|1), the superconformal group in dimension 4,
signature (1,3) and supersymmetry N=1. The quantization is done by substituting
the groups and homogeneous spaces by their quantum deformed counterparts. The
calculations are done in Manin's formalism. When we restrict to the big cell we
can compute explicitly an expression for the super star product in the
Minkowski superspace associated to this deformation and the choice of a certain
basis of monomials.
