Conversational recommender systems have demonstrated great success. They can accurately capture a user's current detailed preference -- through a multi-round interaction cycle -- to effectively guide users to a more personalized recommendation. Alas, conversational recommender systems can be plagued by the adverse effects of bias, much like traditional recommenders. In this work, we argue for increased attention on the presence of and methods for counteracting bias in these emerging systems. As a starting point, we propose three fundamental questions that should be deeply examined to enable fairness in conversational recommender systems.