This paper investigates whether the use of Constraint Programming (CP) could enable the development of a generic and easy-to-upgrade placement service for Fog Computing. Our contribution is a new formulation of the placement problem, an implementation of this model leveraging Choco-solver and an evaluation of its scalability in comparison to recent placement algorithms. To the best of our knowledge, our study is the first one to evaluate the relevance of CP approaches in comparison to heuristic ones in this context. CP interleaves inference and systematic exploration to search for solutions, letting users on what matters: the problem description. Thus, our service placement model not only can be easily enhanced (deployment constraints/objectives) but also shows a competitive tradeoff between resolution times and solutions quality.