Generally yes, the CEO can fire (or in larger companies, more likely have fired) anyone he or she wants. There can be restrictions, that typically based on employees with a contract.
Did Steve Jobs leave his daughter any money?
Lisa Brennan-Jobs, now a 42 year old author and a Harvard graduate, had a different experience growing up with her father than her half-siblings. After his death, Steve Jobs did make sure to leave Lisa with a multi-million dollar inheritance.