We have studied the energy-transfer dynamics in chromatophores of Rhodobacter sphaeroides and Rhodospirillum rubrum at 77 K, with functional charge separation. Using low-intensity picosecond absorption recovery, we determined that transfer between the energetically low-lying antenna component BCh1896 and the special pair of the reaction center occurs with a time constant of 37 ps in Rb. sphaeroides and 75 ps in R. rubrum. Assuming that a F6rster energy-transfer mechanism applies to the process, this allows us to estimate the distance between BCh1896 in the B875 complex and the special pair P870 in the reaction center to range between 26 and 39/~, in Rb. sphaeroides. Such a distance indicates that the BChI896 pigment and the special pair of the reaction center are at the minimum separation allowed by the size and shape of the reaction center and the light-harvesting polypeptides.