Does the board of directors have an ethical responsibility to reprimand the chair of the board if ...

Yes One of the responsibilities of a board is to imbed hypernorms in the corporate values system (Chapter 5) and to guide corporation into develop and maintain an ethical corporate culture (Chapter 5). It is the responsibility of the board to manage risk, including ethical and reputation risk, and the CEO and Chair at Lululemon both represented reputation and ethical risks. Usually, the board can hire a CEO and Chair; so reprimanding and firing them are also responsibilities. At Lululemon, however, in June 2014, Chair Wilson held nearly 27 of the company shares, and threatened to use that stake to oppose the election of two directors. (Lee 2014) This imbalance in shareholder power may have contributed to Lululemon problems, because it raised obstacles to achieving an independent board able to control Wilson. Ironically, Wilson said he lacked confidence in the board, a PR gaff hours before a shareholder meeting (Friesner 2014).