  Paley-Wiener type theorems describe the image of a given space of functions,
often compactly supported functions, under an integral transform, usually a
Fourier transform on a group or homogeneous space. Several authors have studied
Paley-Wiener type theorems for Euclidean spaces, Riemannian symmetric spaces of
compact or non-compact type as well as affine Riemannian symmetric spaces. In
this article we prove a Paley-Wiener theorem for homogeneous line bundles over
a compact symmetric space $U/K$. The Paley-Wiener theorem characterizes f with
sufficiently small support in terms of holomorphic extendability and
exponential growth of their Fourier transforms. An important tool is a
generalization of Opdam's estimate for the hypergeometric functions for
multiplicity functions that are not necessarily positive. The domain where this
estimate is valid is also bigger. This is done in an appendix.
