"This has always been my dream," comic Brian Kiley said Wednesday night on CBS's "Late Show." "To be on 'The Bruce Willis Show.'"

Kiley was right: David Letterman was out, and Bruce Willis was in. At least for one night.

For the first time since his recovery from open-heart surgery in 2000, Letterman, 55, was missing from the "Late Show" Wednesday -- this time because of an eye infection, Reuters reports.

The absence meant that Willis, 47 (who initially was just going to make an appearance and plug his new movie) stepped in as the night's guest host. The actor held his own, chatting with CBS newsman Dan Rather about his exclusive interview with Saddam Hussein, and then welcoming Kiley, guest Carmen Electra and Grammy-winner John Mayer.

Wednesday was Letterman's first absence since his recovery from open-heart surgery in January of 2000. He missed several weeks of shows and a rotating crop of guest hosts stepped in for a few weeks.

A statement released by Letterman's production company, Worldwide Pants, quotes the TV star's physician, Dr. Louis Aronne, as saying, "Dave has an infection of his right eye. It's under treatment and we expect a full recovery."

Dave acknowledged on Tuesday night's show that his eye was puffy: "I look like somebody gave me a beating," he said. "It's either an irritation, inflammation or infection ... For the love of God, does it hurt!"

In the meantime, "Late Show" will air repeats the rest of this week and will be dark all next week, producers said.