  We present a polynomiality property of the Littlewood-Richardson coefficients
c_{\lambda\mu}^{\nu}. The coefficients are shown to be given by polynomials in
\lambda, \mu and \nu on the cones of the chamber complex of a vector partition
function. We give bounds on the degree of the polynomials depending on the
maximum allowed number of parts of the partitions \lambda, \mu and \nu. We
first express the Littlewood-Richardson coefficients as a vector partition
function. We then define a hyperplane arrangement from Steinberg's formula,
over whose regions the Littlewood-Richardson coefficients are given by
polynomials, and relate this arrangement to the chamber complex of the
partition function. As an easy consequence, we get a new proof of the fact that
c_{N\lambda N\mu}^{N\nu} is given by a polynomial in N, which partially
establishes the conjecture of King, Tollu and Toumazet that c_{N\lambda
N\mu}^{N\nu} is a polynomial in N with nonnegative rational coefficients.
