Looking on the internet deeply has found these results:

private chef is the most popular phrase on the web.

private cook 183,800 results on the web	private chef 13,100,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	Your own personal private chef Roblé. 'Cause we have a private chef in the office. Think about this, you and me on our private plane, flown by our private pilot, eating our private meal, cooked by our private chef. Two months ago, I booked a private chef, musicians the works... for a romantic dinner at home. I'm here to interview for the private chef position. You don't want to eat, but your food is made by a private chef. I haven't actually read your book... but you can't tell me that survival isn't easier for people... who are born with a private chef and health insurance.

private cook

183,800 results on the web

private chef

13,100,000 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

Your own personal private chef Roblé.
'Cause we have a private chef in the office.
Think about this, you and me on our private plane, flown by our private pilot, eating our private meal, cooked by our private chef.
Two months ago, I booked a private chef, musicians
the works... for a romantic dinner at home.
I'm here to interview for the private chef position.
You don't want to eat, but your food is made by a private chef.
I haven't actually read your book... but you can't tell me that survival isn't easier for people... who are born with a private chef and health insurance.