Safety cases are used to argue that safety-critical systems satisfy the properties determined to mitigate the potential hazards in the systems deployment environment. Although primarily a manual task, safety cases have been successfully created for single systems. However, when systems with a high number of configurations are considered, typically developed as a Product Line (PL), considering each possible configuration and constructing sound and complete safety-case argumentation is challenging. This paper presents a novel and general approach for the construction of a safety case for an arbitrary PL that is based on Contract-Based Specification (CBS) of the PL. Starting from a general CBS framework, a PL extension of the CBS framework is presented and it is shown that the extension preserves the properties of the original framework. Then, given a CBS specification of a PL, a set of transformation rules for the construction of the safety case argumentation-structure is defined. Finally, the approach is exemplified on a simplified, but real, and currently produced system by Scania CV AB.