Measurements of electrical conductance in double-stranded DNA suggest that the backbones mediate the long-distance conduction in dsDNA, contrary to the common wisdom in DNA electronics. Understanding charge transport in DNA molecules is a long-standing problem of fundamental importance across disciplines(1,2). It is also of great technological interest due to DNA's ability to form versatile and complex programmable structures. Charge transport in DNA-based junctions has been reported using a wide variety of set-ups(2-4), but experiments so far have yielded seemingly contradictory results that range from insulating(5-8)or semiconducting(9,10)to metallic-like behaviour(11). As a result, the intrinsic charge transport mechanism in molecular junction set-ups is not well understood, which is mainly due to the lack of techniques to form reproducible and stable contacts with individual long DNA molecules. Here we report charge-transport measurements through single 30-nm-long double-stranded DNA (dsDNA) molecules with an experimental set-up that enables us to address individual molecules repeatedly and to measure the current-voltage characteristics from 5 K up to room temperature. Strikingly, we observed very high currents of tens of nanoamperes, which flowed through both homogeneous and non-homogeneous base-pair sequences. The currents are fairly temperature independent in the range 5-60 K and show a power-law decrease with temperature above 60 K, which is reminiscent of charge transport in organic crystals. Moreover, we show that the presence of even a single discontinuity ('nick') in both strands that compose the dsDNA leads to complete suppression of the current, which suggests that the backbones mediate the long-distance conduction in dsDNA, contrary to the common wisdom in DNA electronics(2-4).