Well, "Executive Chef" is classically defined as one who supervises/manages more than one kitchen. To get to this stage you need to show your potential employers that you can competantly manage--keep food and labour costs in line, and put out consistantly good food-- in thier kitchens.
To do that you need to have experience doing similiar postions under your belt.
Key word here is experience.
School will give you knowledge, but not working experience.
Personal chef is almost more about marketing than it is about cooking.
Hope this helps