A Heisenberg model for a S = 1 antiferromagnetic chain, which takes simultaneously into account two alternating exchange parameters, J(1) and J(2), and a single-ion anisotropy parameter, D, is developed by using the Bonner-Fisher procedure. The magnetic susceptibility and specific heat properties of this system as function of alpha = J(2)/J(1) and beta = D/J(1) are discussed. For the susceptibility data, rational unified expressions which reproduce in a satisfactory manner the theory are proposed and used to analyze the magnetic behavior of the alternating chain system Ni-2(EDTA). 6H(2)O. The fit of the data agrees with the presence of a weak dimerization for the Ni(II) chain (alpha = 0.9). On the other hand, comparable values for exchange and single-ion anisotropy parameters are found(J(1)/k = -8 K; beta similar to 1). These results are supported by the specific heat data. In particular, a good agreement between the exchange parameters determined from the two complementary experiments is obtained.