A calculation in the tight-binding approximation, of the static polarizability of an argon atom in solid argon is presented. A linear variational technique is used to estimate the polarizability. The results are given as a function of the lattice parameter. The predicted polarizability at the normal solid density at T = 0°K is about 6% less than the free-atom value. For an increase in density accessible to pressure measurements of the static dielectric constant, an additional decrease of 4% in the polarizability is predicted. The relevance of these results to an a priori calculation of an interatomic potential for solid argon is discussed.