To cleave DNA, the single polypeptide restriction-modification enzyme LlaGI must communicate between a pair of indirectly repeated recognition sites. We demonstrate that this communication occurs by a 1-dimensional route, namely unidirectional dsDNA loop translocation rightward of the specific recognition sequence 5'-CTnGAyG-3' as written (where n is either A, G, C or T and y is either C or T). Motion across thousands of base pairs is catalysed by the helicase domain and requires the hydrolysis of 1.5-2 ATP per base pair. DNA loop extrusion is accompanied by changes in DNA twist consistent with the motor following the helical pitch of the polynucleotide track. LlaGI is therefore an example of a polypeptide that is a completely self-contained, multi-functional molecular machine.