  We define and compute the leading sphere diagram contribution to the entropy
of the BTZ black hole supported by Kalb-Ramond flux in bosonic string theory.
In a winding condensate description, integrating exactly over the constant mode
for the radial direction of AdS$_3$ reduces the problem to one of the
correlation functions of winding operators in the free theory. The volume of
the residual PSL(2,$\mathbb{C}$) gauge group of the sphere is canceled by the
action of conformal transformations on the winding interaction insertions. We
formulate a precise version of the replica trick in terms of (infinitesimally)
non-integer winding condensates to produce the entropy of the BTZ black hole.
The resulting entropy can be calculated from the one-point function of a
non-local operator on the worldsheet.
