Analysis of O2 binding equilibria by two independent groups has suggested that the affinity for binding the fourth O2 to Hb tetramers is very high, about 800-1200 cal/mol higher than that of dimers (Chu, A. H., Turner, B. W., and Ackers, G. K. (1984) Biochemistry 23, 604-167; Di Cera, E., Robert, C. H., and Gill, S. J. (1987) Biochemistry 26, 4003-4008). Recently, Gibson and Edelstein challenged the reality of the quaternary enhancement effect, based on kinetic data (Gibson, Q. H., and Edelstein, S. J. (1987) J. Biol. Chem. 262, 516-519). However, these studies failed to directly address the key issue of the relative affinities of dimers and alpha 2 beta 2(O2)3. Furthermore, the extent to which alpha/beta differences influence these results remains an open question. Using partial laser photolysis and O2/CO replacement techniques we have, for the first time, resolved the rates of O2 association and dissociation to both alpha and beta chains within "R state" tetramers and dimers. We find that the beta chains are faster than alpha for both O2 binding (approximately 2-fold) and release (approximately 3-fold). The kinetically determined O2 affinities derived from these data are essentially identical for dimers and alpha 2 beta 2(O2)3. That is, the data do not show significant quaternary enhancement and suggest that the equilibrium data have both overestimated the affinity of alpha 2 beta 2(O2)3 and underestimated the affinity of dimers. The significance of and possible origins for the discrepancy between equilibrium and kinetic data are discussed.