One of the major applications of generative models for drug discovery targets the lead-optimization phase. During the optimization of a lead series, it is common to have scaffold constraints imposed on the structure of the molecules designed. Without enforcing such constraints, the probability of generating molecules with the required scaffold is extremely low and hinders the practicality of generative models for de novo drug design. To tackle this issue, we introduce a new algorithm, named SAMOA (Scaffold Constrained Molecular Generation), to perform scaffold-constrained in silico molecular design. We build on the well-known SMILES-based Recurrent Neural Network (RNN) generative model, with a modified sampling procedure to achieve scaffold-constrained generation. We directly benefit from the associated reinforcement learning methods, allowing to design molecules optimized for different properties while exploring only the relevant chemical space. We showcase the method's ability to perform scaffold-constrained generation on various tasks: designing novel molecules around scaffolds extracted from SureChEMBL chemical series, generating novel active molecules on the Dopamine Receptor D2 (DRD2) target, and finally, designing predicted actives on the MMP-12 series, an industrial lead-optimization project.