Software product lines are increasingly used to handle the growing demand of custom-tailored software variants. They provide systematic reuse of software paired with variability mechanisms in the code to implement whole product families rather than single software products. A common domain of application for product lines are safety-critical systems, which require behavioral correctness to avoid dangerous situations in-field. While most approaches concentrate on post-hoc verification for product lines, we argue that a stepwise approach to create correct programs may be beneficial for developers to manage the growing variability. Correctness-by-construction is such a stepwise approach to create programs using a set of small, tractable refinement rules that guarantee the correctness of the program with regard to its specification. In this paper, we propose the first approach to develop correct-by-construction software product lines using feature-oriented programming. First, we extend correctness-by-construction by two refinement rules for variation points in the code. Second, we give a proof for the soundness of the proposed rules. Third, we implement our technique in a tool called VarCorC and show the applicability of the tool by conducting two case studies.