  We use radial quantization to compute Chern-Simons partition functions on
handlebodies of arbitrary genus. The partition function is given by a
particular transition amplitude between two states which are defined on the
Riemann surfaces that define the (singular) foliation of the handlebody. The
final state is a coherent state while on the initial state the holonomy
operator has zero eigenvalue. The latter choice encodes the constraint that the
gauge fields must be regular everywhere inside the handlebody. By requiring
that the only singularities of the gauge field inside the handlebody must be
compatible with Wilson loop insertions, we find that the Wilson loop shifts the
holonomy of the initial state. Together with an appropriate choice of
normalization, this procedure selects a unique state in the Hilbert space
obtained from a K\"ahler quantization of the theory on the constant-radius
Riemann surfaces. Radial quantization allows us to find the partition functions
of Abelian Chern-Simons theories for handlebodies of arbitrary genus. For
non-Abelian compact gauge groups, we show that our method reproduces the known
partition function at genus one.
