In the endeavour to scale up the number of qubits in an ion-based quantum computer several groups have started to develop miniaturised ion traps for extended spatial control and manipulation of the ions. Shuttling and separation of ion strings have been the foremost issues in linear-trap arrangements and some prototypes of junctions have been demonstrated for the extension of ion motion to two dimensions. While junctions require complex trap structures, small extensions to the one-dimensional motion can be accomplished already in linear trap arrangements. Here, control of the extended field in a planar, linear chip trap is used to shuttle ions in two dimensions. With this approach, the order of two or more ions in a string can be reversed. The control over individual ion positions in a linear trap presents a new tool for ion-trap quantum computing. It is also expected to work with mixed crystals of different ion species and as such could have applications for sympathetic cooling of an ion string.