I think the following summary and the rest of the article from BetterBoards kind-of goes without saying but if that were the case, we wouldn't need to say it. Please read.
According to BetterBoards (austrailian "BoardSource" Both the Board and the CEO have a duty to act in the best interests of the organisation as a whole. Therefore, the separate roles and distinct responsibilities of the CEO/Board relationship should exist in an environment of teamwork, communication and mutual respect. A healthy and efficient relationship is essential for successfully achieving organisational goals. In particular, a strong, productive relationship between the CEO and the Chair of the Board will support improved corporate performance. Consideration should be given to the obligations which both parties owe to each other, in order to successfully reach a common organisational outcome. A productive CEO/Board relationship is one of negotiation, and a successful negotiator knows not to enter without considering the other party’s needs and perceptions, as well as their own.