Tricyclic scaffolds structurally related to the well‐known benzodiazepine class of drugs show diverse biological activities strikingly different from those of their benzodiazepine counterparts. Interested by this scaffold‐hopping perspective, we previously developed a continuous‐flow method for the conversion of benzodiazepinediones into oxazoloquinolinones. Attempted extension of this synthetic route to the corresponding oxazolonaphthyridinone scaffolds met with limited success, however. This encouraged us to develop a different approach to pyridine‐based tricyclic motifs. In line with our interest in scaffold hopping, in this paper we describe a general, convergent [3+3] cyclocondensation approach to [1,3]oxazolo[4,5‐c]‐1‐naphthyridin‐4(5H)‐ones. The key synthetic steps in this approach are: (1) the construction of an amide linkage connecting two peripheral heterocycles; and (2) a palladium‐catalysed intramolecular C–H arylation to complete the tricyclic scaffold.