This paper introduces a continuous-time extension to the influential CreditRisk+ model for portfolio credit risk modeling. For capital calculations it introduces a risk measure based on the maximum of the loss process of a portfolio over a specified time interval. An extensive numerical study demonstrates that this extension provides an accurate risk assessment. The new framework has many advantages. First, it enables loss evaluation over a continuous time period rather than at a fixed point in time as in the original CreditRisk+ model. Second, the framework offers great flexibility, for example, for the incorporation of collateral risks, interest income and regime shifts. It also accommodates the calibration of almost any observed dependence between counterparties, including dependencies of the form used in structural credit risk models. Finally, the framework establishes a direct connection to insurance industry ruin theory models, allowing the model to leverage exact results and established algorithms from this field to efficiently and accurately determine the credit loss distribution within the continuous-time framework. This extended model therefore provides a comprehensive and theoretically robust approach to assessing credit risk over time and shows the potential for broader use in risk management.