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In the classical Chapman-Enskog theory of a fully ionized gas, the transport coefficients evolve as functionals of certain weighted total scattering cross sections. If a Coulomb potential is assumed between scattering particles, these scattering integrals diverge. A common procedure to circumvent this difficulty is to integrate the Coulomb results up to the Debye cutoff. A more appropriate procedure involves the use of the shielded Coulomb potential, in which case the scattering integrals converge, and there is no need to introduce a cutoff. These integrals are calculated using the shielded Coulomb potential and the resultant transport coefficients are compared with those of the standard ``Coulomb plus Debye cutoff'' calculations. To the ``dominant log term'' the two procedures give identical results. To terms of the next order of accuracy for the viscosity and thermal conductivity the difference between the two formulations is of the order of 0.5%, and for the diffusion and electrical conductivity the difference is of the order of 2%. The major calculation is that of the classical cross section for the screened Coulomb potential.