Before Kevin Costner became one of the biggest movie stars in the world, he wasn't even sure he wanted to be an actor. Then, by chance, he talked to one of the biggest movie stars in the world.

When he was just 22-years-old, Costner and his new bride, Cindy, were returning from their honeymoon in Puerto Vallarta. On the same plane, sitting all by himself in an empty row, sat seven-time Oscar nominee Richard Burton.

Costner had been working in marketing, while dabbling in community theater. Though he felt that acting and storytelling might be his true calling, his conservative, blue collar upbringing (his dad was literally a ditch digger) prevented Costner from fully embracing the dream.

[Related: Kevin Costner Passes the Leading Man Torch to 'Jack Ryan' Co-Star Chris Pine]

The now world-famous actor was filled with internal conflict when he saw Burton on that plane. After Costner approached the lauded actor, Burton convinced him to do more than dabble.

"He was famously volatile, he was incredibly talented, and he could have easily said, 'Please go sit back in your seat, that's why I bought all these seats around me, so no one would talk to me.' But he didn't do that, and he easily could have," Costner told us over the phone yesterday while discussing his latest role, playing Thomas Harper, young Jack Ryan's (Chris Pine) CIA handler in this weekend's "Jack Ryan: Shadow Recruit."

"[Burton had] a gentleness with me. I was really unsure what I wanted to do with my life, and I saw him there, and I intruded on his," said Costner. "I had never been in a play, well, that's not true I had done some community theater, but I was really thinking I could make this a living and I desperately wanted to talk to him. The conversation never really expanded other than there was a gentleness and a kindness, and looking at me saying, 'I think you should try this.’”

See Kevin Costner and Chris Pine in a clip from "Jack Ryan: Shadow Recruit":

After the conversation ended and the plane landed, Costner and his wife realized they'd forgotten about airport taxes, and they didn't have enough money to get home to Orange County, CA. While sitting on their suitcases, trying to figure out a way home, a limousine stopped in front of the couple. The window rolled down, and Burton wished the Costners good luck.

If Burton got a chance to see Costner's work, we'll never know for sure, but the odds aren't good. Burton died in 1984; Costner's big break didn't happen until Lawrence Kasdan's "Silverado" in 1985. However, Burton may very well have seen his young protégé's scarred wrist in Kasdan's "The Big Chill," which Costner was famously cut out of in 1983. Either way, Costner and Burton's airplane conversation was their first and last.

“The crime was that we never spoke again. I was probably 22-years-old. I didn't make my first check till I was probably 27, 28, and he might have been gone by then, or not. At first I didn't want to circle back, it's just not how I operate. But that would have been a nice conversation for me."

[Related: 'Jack Ryan: Shadow Recruit' Megaclip With Chris Pine, Kevin Costner, and a Quasi-Personal Dog]

Indeed, it would have been an interesting story. Regardless, we're just glad Burton and Costner met at all. Because in some small way it allowed Costner to find the strength to tell so many more interesting stories.

You can see Costner help tell another one when "Jack Ryan: Shadow Recruit" opens wide this Friday.

See an exclusive clip from "Jack Ryan: Shadow Recruit":