In the presence of condensing agents, single chains of giant double-stranded DNA undergo a first-order phase transition between an elongated coil state and a folded compact state. To connect this like-charged attraction phenomenon to counterion condensation, we performed a series of single-chain experiments on aqueous solutions of DNA, where we varied the extent of counterion condensation by varying the relative dielectric constant epsilon(r) from 80 to 170. Single-chain observations of changes in the conformation of giant DNA were performed by transmission electron microscopy and fluorescence microscopy, with tetravalent spermine (SPM(4+)) as a condensing agent. At a fixed dielectric constant, single DNA chains fold into a compact state upon the addition of spermine, whereas at a constant spermine concentration single DNA chains unfold with an increase in epsilon(r). In both cases, the transition is largely discrete at the level of single chains. We found that the critical concentration of spermine necessary to induce the single-chain folding transition increases exponentially as the dielectric constant increases, corresponding to 87-88% of the DNA charge neutralized at the onset of the transition. We also observed that the toroidal morphology of compact DNA partially unfolds when epsilon(r) is increased.