We have performed restriction mapping of DNA molecules using restriction endonucleases in nanochannels with diameters of 100-200 nm. The location of the restriction reaction within the device is controlled by electrophoresis and diffusion of Mg2+ and EDTA. We have successfully used the restriction enzymes SmaI, SacI, and PacI, and have been able to measure the positions of restriction sites with a precision of approximately 1.5 kbp in 1 min using single DNA molecules.