  We investigate the Kosterlitz-Thouless transition for hexatic order on a
fluctuating spherical surface of genus zero and derive a Coulomb gas
Hamiltonian to describe it. In the Coulomb gas Hamiltonian, charge densities
arises from disclinations and from Gaussian curvature. There is an interaction
coupling the difference between these two densities, whose strength is
determined by the hexatic rigidity. We then convert it into the sine-Gordon
Hamiltonian and find a linear coupling between a scalar field and the Gaussian
curvature. After integrating over the shape fluctuations, we obtain the massive
sine-Gordon Hamiltonian, which corresponds to a neutral Yukawa gas, and the
interaction between the disclinations is screened. We find, for $K_{A}/\kappa
\gg 1/2$ where $K_{A}$ and $\kappa$ are hexatic and bending rigidity,
respectively, the transition is supressed altogether, much as the
Kosterlitz-Thouless transition is supressed in an infinite 2D superconductor.
If on the other hand $K_{A}/\kappa \ll 1/2$, there can be an effective
transition.
