Coupled cluster computations using large basis sets and the Douglas-Kroll Hamiltonian for relativistic effects are reported for the dipole polarizability, alpha, of the sodium atom. Our best value of alpha(Na)/e(2)a(0)(2)E(h)(-1) = 162.88 +/- 0.6 is in excellent agreement with the value obtained by atomic-beam interferometry, thus resolving a persistent discrepancy between theory and experiment. Combining our alpha(Na) with a very accurate value of alpha(Li), we find that alpha(Li)/alpha(Na) = 1.0071 +/- 0.0037 establishing that alpha(Li) is greater than alpha(Na). (C) 2004 Elsevier B.V. All rights reserved.