We describe combined AFM/Raman measurements on single nanodumbbells, consisting of silver nanospheres linked with dibenzyl-4,4'-dithiol (DBDT). The measured surface-enhanced Raman scattering (SERS) enhancement factor, EFexp = 3 x 10(7) at 532 nm, corresponds to the observed signal strength of a single DBDT molecule, the Raman cross section of which was determined to be d sigma/d Omega = 6 x 10(-28) cm(2)/sr. We show that the product of the local field enhancement, EFP = (E-i/E-0)(2)(E-s/E-0)(2) = 3 x 10(6), and the chemical contribution due to reduced detuning, EFC = (Delta(0)/Delta)(2) = 12, account for the observed effect. The chemical contribution is assessed by exploring model structures Ag-n-S-DB-S-Ag-m (n, m = 0, 3, 7, 20). The pi-pi* transition at 287 nm, which determines the polarizability of the bare molecule, acquires a DBDT-to-silver charge-transfer character upon binding to silver. The CT transition near 400 nm reduces the detuning but remains nonresonant at 532 nm. We observe a soft polarization dependence, which suggests optical activity, which in part is ascribed to coupling between plasmons and conjugated electrons of DBDT. Modest enhancement factors are sufficient to detect single molecules through nonresonant SERS.