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Previous measurements of the electronic conductance of DNA nucleotides or amino acids have used tunnel junctions in which the gap is mechanically adjusted, such as scanning tunneling microscopes or mechanically controllable break junctions. Fixed-junction devices have, at best, detected the passage of whole DNA molecules without yielding chemical information. Here, we report on a layered tunnel junction in which the tunnel gap is defined by a dielectric layer, deposited by atomic layer deposition. Reactive ion etching is used to drill a hole through the layers so that the tunnel junction can be exposed to molecules in solution. When the metal electrodes are functionalized with recognition molecules that capture DNA nucleotides via hydrogen bonds, the identities of the individual nucleotides are revealed by characteristic features of the fluctuating tunnel current associated with single-molecule binding events.