 After completing Peacock Military Academy, Elizondo enrolled at St. Mary's University in San Antonio, where he majored in chemistry, earning a Bachelor of Science degree.Though he had considered a career in medicine, he felt called to serve in the ministry and enrolled in Assumption Seminary in San Antonio, so that he could stay close to his home.Elizondo was ordained as a priest of the Archdiocese of San Antonio in 1963 by Robert E. Lucey, its archbishop.