Define “Top-Tier” as you will. Can you reach that level simply through slogging it out in the kitchens, learning from the best, mastering the techniques, etc.? Or does any restaurant worth its salt require its executive/sous/whatever chef have a degree from a culinary institute?
Looking in Wikipedia, it appears that Thomas Keller never attended culinary school. So yes, it’s possible.
Also, Jacques Pépin.
You don’t have to. Art Smith is a pretty well-known and successful chef who didn’t go to culinary school.
If you want a more haute cuisine chef, Ludo Lefebvre also trained in kitchens and not in culinary schools.
“Require?” No. Not in America. In France and Switzerland, a more structured educational and reference system is in place.
I don’t know what percentage of people employed as chefs have a degree but it’s far short of 100%.
Heston Blumenthal
has no formal culinary training and his flagship restaurant has 3 Michelin stars and has been named best restaurant in the world.
Becoming a celebrity is mostly a matter of skill at self promotion, not at doing whatever. Applies to chefs as much as any other activity.
A promising self-taught chef might have a hard time being hired at the upper tiers of the established industry. But that’s no obstacle to starting his/her own restaurant and, given enough talent, drive and luck, having it succeed greatly and thereby propel them into the recognized top tier.
Some of the names mentioned may not have attended culinary school, but they have gone through apprenticeships. I’d say that’s still formal training.
I find it hard to believe that anyone could reach the top of their profession without at least having some opportunity to learn from others. Is that an apprenticeship? It may not be formal, but I think that most “top chefs” started in someone else’s kitchen. There are things that you simply cannot learn from books.
This is just my guess, but I would think MORE of the “best” chefs apprenticed with other master chefs than went through culinary school. It’s also a matter of opinion as to what constitutes an, er, “top chef.” Art Smith is known for, basically, really well done soul food; Ludo for combining exacting French technique with newer techniques loosely and inaccurately sometimes called “molecular gastronomy;” Keller for continuing and extending Alice Waters’ emphasis on fresh local ingredients; Blumenthal originally for the nose-to-tail concept; and so forth. Which is really at the top of their profession? All of them?
And there is a self promotion element as LSL Guy notes. Did the four named just have good press agents? Maybe. And I don’t think anyone really thinks Guy Fieri or even Michael Mina is a great chef.
If you are a good chief, your parking lot will be full. And other restaurants would see that! Would be more than willing to have their parking lots full as well.
McDonalds’ parking lots are also full.
That is a clue that people like their food! Also a clue people like their French fries - some restaurants have tried giving people french fries without peeling off the skins (LAZY! CHEAP!).
I point out how busy McDonalds is and how many French fries they sell…
(The “cook” there is located at their corporate headquarters and would be a good one to hire if you want a successful product.)
Perhaps it only applies to the Western [ French ] Tradition. I would find it unlikely the great Chinese chefs of Ancient China, who prepared a 100 courses — and the Chinese are the only rivals to Americans as great eaters — or the Hawaiians, or the Aztecs, or North Africans ever had cookery schools.
Mighty trenchermen all.
In theory, you only have to cook one dish superlatively well to get a good reputation. Cooking school helps, probably, but if you put 10,000 hours into teaching yourself to cook there are many excellent books and videos on it. Unless you want to cook in a prestigious restaurant there are alternatives.
The ONLY worthwhile French fries include the skins. 
:dubious:
Make America Eat Great Again.
Or at least eat huuuugely.
Oddly enough that may be the campaign slogan most able to be implemented in the next 4 years. 