Using Chandra archival data, we quantify the evolution of cluster morphology with redshift. Clusters form and grow through mergers with other clusters and groups, and the amount of substructure in clusters in the present epoch and how quickly it evolves with redshift depend on the underlying cosmology. Our sample includes 40 X-ray selected, luminous clusters from the Chandra archive, and we quantify cluster morphology using the power ratio method (Buote & Tsai 1995). The power ratios are constructed from the moments of the X-ray surface brightness and are related to a cluster's dynamical state. We find that, as expected qualitatively from hierarchical models of structure formation, high-redshift clusters have more substructure and are dynamically more active than low-redshift clusters. Specifically, the clusters with z>0.5 have significantly higher average third and fourth order power ratios than the lower redshift clusters. Of the power ratios, $P_3/P_0$ is the most unambiguous indicator of an asymmetric cluster structure, and the difference in $P_3/P_0$ between the two samples remains significant even when the effects of noise and other systematics are considered. After correcting for noise, we apply a linear fit to $P_3/P_0$ versus redshift and find that the slope is greater than zero at better than 99% confidence. This observation of structure evolution indicates that dynamical state may be an important systematic effect in cluster studies seeking to constrain cosmology, and when calibrated against numerical simulations, structure evolution will itself provide interesting bounds on cosmological models.

42 pages, 6 figures, ApJ accepted. For a version of the paper containing an appendix with images of all of the clusters, see http://www.ociw.edu/~tesla/structure.ps.gz