  We consider the correlation function of a circular Wilson loop with two local
scalar operators at generic 4-positions in planar N=4 supersymmetric gauge
theory. We show that such correlator is fixed by conformal invariance up to a
function of 't Hooft coupling and two scalar combinations of the positions
invariant under the conformal transformations preserving the circle. We compute
this function at leading orders at weak and strong coupling for some simple
choices of local BPS operators. We also check that correlators of an infinite
line Wilson loop with local operators are the same as those for the circular
loop.
