Five Star Chinese Restaurant in Washington DC and NYC?

I heard there is this five star chinese restaurant that only famous people could go to. I heard that Princess Diana ate there. The restaurant has the patron's name engraved in the chopsticks and they are given the same chopsticks back when they return for another meal. If a person were to pass away, they would honor their chopsticks by displaying it somewhere. I heard it's only in NYC and Washington DC. What kind of restaurant is this? What is the name of it?