Tipping a private chef is recommended based on a percentage of the total cost of their services. For most private chef services, a minimum tip percentage of 15 to 20% is suggested. I understand that you're asking this question because you appreciate the service you've received and want to do the right thing. The right thing here is whatever you want it to be. As Dario clearly states, there is no tip requirement.
You couldn't leave a tip and be okay. However, if you personally want to show additional gratitude, simply choose an amount that fits your budget and your idea of what you want to do. When it comes to tipping a private chef, it's usually common to leave between 15 and 20% of the cost of the service as a tip. This percentage can be adjusted depending on the level of service provided and your overall satisfaction.
When it comes to showing appreciation, for service, or when a chef provides help in the kitchen, giving a more generous tip is a wonderful way to express gratitude.