No, it is NOT acceptable to put this on a 1099. You SHOULD have withheld FICA taxes, Federal income taxes at 25%, and any state income taxes from the check. Now you are faced with the tasteless task of recovering the unwithheld tax from the employee OR adding the FICA taxes that you should have withheld to the gross payment and including those on the employee's W-2. You may also be facing penalties from the IRS for not withholding the statutory 25% Federal income tax from the bonus.
Next time, tell the CEO that it MUST go through payroll since that's what the law requires.