  We consider a supersymmetric Wilson loop operator for 4d N=4 super Yang-Mills
theory which is the natural object dual to the AdS_5 x S^5 superstring in the
AdS/CFT correspondence. It generalizes the traditional bosonic 1/2 BPS
Maldacena-Wilson loop operator and completes recent constructions in the
literature to smooth (non-light-like) loops in the full N=4 non-chiral
superspace. This Wilson loop operator enjoys global superconformal and local
kappa-symmetry of which a detailed discussion is given. Moreover, the
finiteness of its vacuum expectation value is proven at leading order in
perturbation theory. We determine the leading vacuum expectation value for
general paths both at the component field level up to quartic order in
anti-commuting coordinates and in the full non-chiral superspace in suitable
gauges. Finally, we discuss loops built from quadric splines joined in such a
way that the path derivatives are continuous at the intersection.
