I would first explore other ways to cut your budget - an across the board reduction in pay, layoffs at a more junior level, etc. An organization needs strong leadership during these difficult times and should not be cutting out those that can lead the way out of this economy.

But to directly answer your question, as an employee of an organization, you cannot make the decision to lay yourself off without approval by your employer, i.e. The Board of Directors. You can certainly delicately suggest to the Board that you would be willing to be laid off rather than tender your resignation. This puts the Board in a position, however, not to hire another CEO for a period of time and if self-insured, results in their paying your unemployment benefits. Hopefully, you have a positive relationship with the Board and they will accept your proposal. Good luck!