It has been proposed that single molecules of DNA could be sequenced by measuring the physical properties of the bases as they pass through a nanopore. Theoretical calculations suggest that electron tunnelling can identify bases in single-stranded DNA without enzymatic processing, and it was recently experimentally shown that tunnelling can sense individual nucleotides and nucleosides. Here, we report that tunnelling electrodes functionalized with recognition reagents can identify a single base flanked by other bases in short DNA oligomers. The residence time of a single base in a recognition junction is on the order of a second, but pulling the DNA through the junction with a force of tens of piconewtons would yield reading speeds of tens of bases per second.