The Dances With Wolves star was jetting off on his honeymoon after marrying his first wife, Cindy, in 1978 when he realised he was on the same flight as one of his heroes.

Still unsure about following his acting dreams, Costner plucked up the courage to approach Burton and ask him for advice.

"He got on the plane first and had bought five seats all around him so that no one could sit next to him," he tells WENN. "We all got on the plane and I was burning up inside because I was grappling with the idea of acting, so seeing Richard I thought was a sign. My wife didn't even know that I was burning with this idea of what I was gonna be in my life."

"I remember him reading a book and as I walked over to talk to him, the whole airplane sort of stood up like a wave in a stadium! I looked very young and I said, 'Excuse me sir, when you get a moment can I ask you a bit of advice?' And he looked at me and he was probably thinking, 'Jesus, five seats isn't enough!' He said, 'When I finish reading this book, yes'."

Costner sat patiently watching his hero as he finished his book, Gore Vidal's Lincoln, and then slept - and then Burton called him over for a chat.

"We had a talk that was just between us and then I went and sat back down in my seat," he adds.

But the magical moment didn't end there: "We didn't have a lot of money for our honeymoon and my parents drove us to the airport and we were gonna catch a bus back to the Disneyland hotel. My wife and I were sitting on our suitcases waiting and this big limousine came literally about eight inches from my face and just stopped. The window rolled down and Richard Burton said, 'Good luck', and the window went up and he drove on.

"I never got a chance to ever talk to Richard again so he has no idea what became of me."