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(1,2). Theoretical calculations suggest that electron tunnelling can identify bases in single-stranded DNA without enzymatic processing(3-5), and it was recently experimentally shown that tunnelling can sense individual nucleotides(6) and nucleosides(7). 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.