Context: The paper addresses the use of a Software Product Line approach in the context of developing software for a high-integrity, regulated domain such as civil aerospace. The success of a Software Product Line approach must be judged on whether useful products can be developed more effectively (lower cost, reduced schedule) than with traditional single-system approaches. When developing products for regulated domains, the usefulness of the product is critically dependent on the ability of the development process to provide approval evidence for scrutiny by the regulating authority. Objective: The objective of the work described is to propose a framework for arguing that a product instantiated using a Software Product Line approach can be approved and used within a regulated domain, such that the development cost of that product would be less than if it had been developed in isolation. Method: The paper identifies and surveys the issues relating the adoption of Software Product Lines as currently understood (including related technologies such as feature modelling, component-based development and model transformation) when applied to high-integrity software development. We develop an argument framework using Goal Structuring Notation to structure the claims made and the evidence required to support the approval of an instantiated product in such domains. Any unsubstantiated claims or missing/sub-standard evidence is identified, and we propose potential approaches or pose research questions to help address this. Results: The paper provides an argument framework supporting the use of a Software Product Line approach within a high-integrity regulated domain. It shows how lifecycle evidence can be collected, managed and used to credibly support a regulatory approval process, and provides a detailed example showing how claims regarding model transformation may be supported. Any attempt to use a Software Product Line approach in a regulated domain will need to provide evidence to support their approach in accordance with the argument outlined in the paper. Conclusion: Product Line practices may complicate the generation of convincing evidence for approval of instantiated products, but it is possible to define a credible Trusted Product Line approach.