Directors’ dilemma: beneficiaries of fundraising for a not-for-profit organisation.

In this case study, you are the newly appointed CEO of a not-for-profit organisation, structured as a company limited by guarantee. The board of the organisation consists of seven voluntary, non-executive directors and the non-executive chairman of the board. While not a member of the board, the CEO is secretary to the board and attends all board meetings in that capacity.
You have been approached by the chairman of the board who has asked you to fundraise for a project that the chairman is undertaking. While the organisation itself will be a beneficiary of the project, the main financial and other benefits will accrue directly to the chairman.
Concerned about the chairman’s request, the CEO approaches another long-serving non-executive director to seek advice. The advice the CEO receives is ‘don’t be too worried about it, the chairman has operated like that for years’.
Should the CEO support the chairman’s fundraising efforts?