The purpose of the Energy-Aware COmputing (EACO) Initiative at the University of Bristol is to bring together researchers and engineers with interests in energy-aware computing for discussions to identify intellectual challenges that can be developed into collaborative research projects. We strive to go significantly beyond the state of the art. This Technical Report summarizes the Intellectual Challenges identified a the first EACO workshop on 25 May 2011. It serves as basis for a series of working documents to further develop these challenges. Updates are expected after each future EACO workshop.