A large [21s16p15d7f/11s9p7d3f] basis set consisting of 287 contracted gaussian-type functions yields near-Hartree-Fock non-relativistic values for the mean and the anisotropy of the static dipole polarizability of hydrogen iodide, <(alpha)over bar> = 35.38 and Delta alpha=2.62 e(2)a(0)(2)E(h)(-1). Using a smaller, carefully optimized basis set at the CCSD(T) level of theory, we obtain [<(alpha)over bar>(R) - <(alpha)over bar>(R-e)]/e(2)a(0)(2)E(h)(-1) = 5.15(R - R-e) + 1.42(R - R-e)(2) - 0.44(R - R-e)(3) - 0.57(R - R-e)(4) and [Delta alpha(R) - Delta alpha(R-e)]/ e(2)a(0)(2) E-h(-1) = 10.50(R - R-e) + 3.52(R - R-e)(2) - 0.76(R - R-e)(3) - 0.75(R - R-e)(4) for the behaviour of the polarizability invariants around the equilibrium bondlength R-e = 1.60916 Angstrom. Combining our best values, we propose for the ground vibrational state <(alpha)over bar> = 36.52 and Delta alpha = 2.94 e(2)a(0)(2)E(h)(-1). Even with the inclusion of relativistic effects the theoretical values are not reconcilable with the available experimental data.