In Software Defined Infrastructure (SDI), virtualization techniques are used to decouple applications and higher-level services from their underlying physical compute, storage, and network resources. The approach offers a set of powerful new capabilities (isolation, encapsulation, portability, interposition), including the formation of a software-based, infrastructure-wide control plane for orchestrated management. In this position paper, we identify opportunities for revisiting ongoing cybersecurity challenges using SDI as a powerful new toolset. Benefits of this approach can be broadly utilized in public, private, and hybrid clouds, data centers, enterprise computing, IoT deployments, and more. The discussion motivates the research challenge underlying VMware's partnership with the National Science Foundation to fund novel and foundational research in this area. Known as the NSF/VMware Partnership on Software Defined Infrastructure as a Foundation for Clean-Slate Computing Security (SDI-CSCS), the jointly funded university research program is set to begin in the fall of 2017.