It has been a long-standing problem how to relate Chern–Simons theory to the quantum groups. In this paper we recover the classical r-matrix directly from a three-dimensional Chern–Simons theory with boundary conditions, thus creating a direct link to the quantum groups. It is known that the Jones polynomials can be constructed using an R-matrix. We show how these constructions can be seen to arise directly from 3-dimensional Chern–Simons theory.