This qualitative dissertation explores how the principal's leadership roles build capacity for change and how chaos theory contributes to this understanding. The roles studied include distributive leadership, moral leadership, social justice leadership, democratic leadership, and instructional leadership. The tenets of chaos theory examined include change as nonlinear, feedback loops and fractals, turbulence, complexity, strange attractors, and the butterfly effect. The research participants include three urban Texas high school principals. Each principal had a tenure of three or more years, at a campus with a population of at least 50% children of color, and had structures in place on campus to implement change. Grounded theory was used to code data, including principal interviews, observations, and artifacts. Findings show that capacity building is foundational to school improvement, principal roles are key to a change process's success, and chaos theory can contribute to and highlight our understandings of a campus change process. These findings can better inform principals, principal preparation programs, and districts on meeting the needs of all children. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]