  It is argued that whereas supersymmetry requires the instanton contribution
to the expectation value of a straight Wilson line in the N=4 supersymmetric
SU(2) Yang-Mills theory to vanish, it is not required to vanish in the case of
a circular Wilson loop. A non-vanishing value can arise from a subtle interplay
between a divergent integral over bosonic moduli and a vanishing integral over
fermionic moduli. The one-instanton contribution to such Wilson loops is
explicitly evaluated in semi-classical approximation. The method utilizes the
symmetries of the problem to perform the integration over the bosonic and
fermionic collective coordinates of the instanton. The integral is singular for
small instantons touching the loop and is regularized by introducing a cutoff
at the boundary of the (euclidean) AdS_5 moduli space. In the case of a
circular loop a nonzero finite result is obtained when the cutoff is removed
and a perimeter divergence subtracted. This is contrasted with the case of the
straight line where the result is zero after subtraction of an identical
divergence per unit length. The linear divergence is an artifact of our non
supersymmetric regulator that deserves further consideration. The
generalization to gauge group SU(N) with arbitrary N is straightforward in the
limit of small 't Hooft coupling. The extension to strong 't Hooft coupling is
more challenging and only a qualitative discussion is given of the AdS/CFT
correspondence
