Peter Rowe said he and two friends had just finished racing up the staircase at the Philadelphia Museum of Art when they saw Sylvester Stallone.
"He said to us, 'Man, you guys are fast. You're making me look bad!'," Rowe said.
Stallone then posed for a selfie with the trio, putting up one fist.
"Look tough, guys!" he said, according to Rowe.
Stallone made the art museum's steps famous in his first turn as fictional boxer Rocky Balboa, who used them as part of his training regimen.
Thousands of people visit the steps each year to recreate the run and take pictures with a Rocky statue, which was originally a prop in Rocky III.
Mr Rowe's friends, Jacob Kerstan and Andrew Wright, were visiting him from Azusa Pacific University in greater Los Angeles. Mr Rowe had recently graduated from the university and moved to the Philadelphia area.
Yet in all their time spent in LA, Mr Rowe said, they never saw a famous person.
"What are the chances of meeting him, that celebrity, right there?" he said of the Stallone encounter, calling it "an unreal experience".
Stallone was in Philadelphia for the shooting of Creed, the latest instalment in the Rocky series. It stars Michael B Jordan, who appeared in Fruitvale Station, as the grandson of early Rocky foe Apollo Creed.