Traits support the factoring out of common behaviour, and its integration into classes in a manner that coexists smoothly with inheritance-based structuring mechanisms. We designed the language Chai, which incorporates statically typed traits into a simple Java-inspired base language, and we discuss three versions of the language: Chai1, where traits are only a mechanism for the creation of classes; Chai2 where traits are a mechanism for the creation of classes, and can also introduce types, and Chai3 where traits play a role at runtime, and can can be applied to objects, and change the objects’ behaviour. We give formal models for these languages, outline the proof of soundness, and our prototype implementation.