  We study Chern-Simons Gauge Theory in axial gauge on ${\mathbb R}^3.$ This
theory has a quadratic Lagrangian and therefore expectations can be computed
nonperturbatively by explicit formulas, giving an (unbounded) linear functional
on a space of polynomial functions in the gauge fields, as a mathematically
well-defined avatar of the formal functional integral. We use
differential-geometric methods to extend the definition of this linear
functional to expectations of products of Wilson loops corresponding to
oriented links in ${\mathbb R}^3,$ and derive skein relations for them. In the
case $G=SU(2)$ we show that these skein relations are closely related to those
of the Kauffman bracket polynomial, which is closely related to the Jones
polynomial. We also study the case of groups of higher rank. We note that in
the absence of a cubic term in the action, there is no quantization condition
on the coupling $\lambda,$ which can be any complex number. This is in line
with the fact that the Jones polynomial, in contrast to the manifold invariants
of Witten and Reshetikhin-Turaev, is defined for any value of the coupling. The
appearance of the parameter $e^{\frac1{2\lambda}}$ in the expectations and
skein relations is also natural. Likewise, the extension of the theory to
noncompact groups presents no difficulties. Finally we show how computations
similar to ours, but for gauge fields in two dimensions, yield the Goldman
bracket.
