A galaxys orientation is one of its most basic observable properties. Astronomers once assumed that galaxies are randomly oriented in space, however it is now clear that some have preferred orientations with respect to their surroundings. Chief among these are giant elliptical galaxies found in the centers of rich galaxy clusters. Numerous studies have shown that the major axes of these galaxies often share the same orientation as the surrounding matter distribution on larger scales. Using Hubble Space Telescope observations of 65 distant galaxy clusters, we show for the first time that similar alignments are seen at earlier epochs when the universe was only one-third its current age. These results suggest that the brightest galaxies in clusters are the product of a special formation history, one influenced by development of the cosmic web over billions of years.