With increasing globalization and outsourcing, IT service providers need a way to assess the resilience of their operations (and of their vendors) to understand the impact that various failures can have on their output, and to guide their decisions on where to best invest for remediation. In this paper, we present the Resiliency Maturity Index (RMI), a framework for characterizing and evaluating the resiliency of an IT services organization. The framework consists of (a) a model for capturing the hierarchical component structure of the organization and the relationships among (sub)components, and (b) a method to determine a quantitative score that indicates the overall resiliency maturity of the organization. We describe a case study of the application of RMI to a hypothetical IT service provider organization, based on our experience of applying it to actual real-world delivery centers. We also demonstrate the utility of the RMI framework through various realistic scenarios such as making investment decisions, .assessing the impact of organizational expansion, and outsourcing decisions.