  This paper is about geometric quantization of the Hitchin system. We quantize
a Kahler form on the Hitchin moduli space (which is half the first Kahler form
defined by Hitchin) by considering the Quillen bundle as the prequantum line
bundle and modifying the Quillen metric using the Higgs field so that the
curvature is proportional to the Kahler form. We show that this Kahler form is
integral and the Quillen bundle descends as a prequantum line bundle on the
moduli space. It is holomorphic and hence one can take holomorphic square
integrable sections as the Hilbert space of quantization of the Hitchin moduli
space.
