This paper studies continual learning (CL) of a sequence of aspect sentiment classification (ASC) tasks in a particular CL setting called domain incremental learning (DIL). Each task is from a different domain or product. The DIL setting is particularly suited to ASC because in testing the system needs not know the task/domain to which the test data belongs. To our knowledge, this setting has not been studied before for ASC. This paper proposes a novel model called CLASSIC. The key novelty is a contrastive continual learning method that enables both knowledge transfer across tasks and knowledge distillation from old tasks to the new task, which eliminates the need for task ids in testing. Experimental results show the high effectiveness of CLASSIC.