"Wa" indicates the topic. The topic is omitted when it's obvious from the context, for instance, the same topic continues. Although "Chikin wa suki dewa arimasen" sounds more natural there. See the following example.
Kare wa hanbāgā ga suki desu. Chikin wa suki dewa arimasen.
The second sentence is the same as the one in your example, but it means "He(= kare) doesn't like chicken" here.
Waツ・Ga issue is one of the hardest things to grasp in Japanese grammar even for advanced learners, so you don't need to worry too much about it now if you are a beginner learner.