The legal interests of the CEO and the organization in an investigation can be very different.  The organization, for example, in order to get rid of the problem quickly and with a minimum of organizational damage could very easily throw the CEO under the bus, as they say.  The CEO may need separate counsel to prevent that from happening and your bylaws probably authorize — or even require — it under the indemnification provisions.  The CEO may also be entitled to separate representation under your insurance policy, without regard to specific bylaw provisions.