Parallel coordinates is a well-known technique for visual analysis of high-dimensional data. Although it is effective for interactive discovery of patterns in subsets of dimensions and data records, it also has scalability issues for large datasets. In particular, the amount of visual information potentially being shown in a parallel coordinates plot grows combinatorially with the number of dimensions. Choosing the right ordering of axes is crucial, and poor design can lead to visual noise and a cluttered plot. In this case, the user may overlook a significant pattern, or leave some dimensions unexplored. In this work, we demonstrate how eye-tracking can help an analyst efficiently and effectively reorder the axes in a parallel coordinates plot. Implicit input from an inexpensive eye-tracker assists the system in finding unexplored dimensions. Using this information, the system guides the user either visually or automatically to find further appropriate orderings of the axes.