We show theoretically that the dimension of a polymer chain in the melt, as measured, for example, by the mean-square end-to-end distance or the mean-square radius of gyration, is different from that of an ideal chain, due to the local packing constraint in the melt. Although the scaling of these dimensions with the molecular weight of a polymer remains the same, the effective Kuhn length is renormalized to a larger value. The correction term is shown to be proportional to the ratio of a packing length to some microscopic cut-off length which partially reflects the effects of the local liquid structure. For an athermal binary polymer blend where the packing lengths of the two species differ, the effective Kuhn length for each polymer depends on the composition of the blend.