"We thought it would be cool, just something different to try," said Rob Burnett, the "Late Show" executive producer. "We've been doing the show for so long that anytime you can come up with something new it makes it interesting for us."
The show that airs on Friday, May 14 will be taped early that morning. Typically, Letterman tapes his Friday show on Thursday evening.
The other days of the week, Letterman tapes his show about six hours before it is aired on CBS.
The show will probably set up remote cameras, perhaps in Times Square, and show other street scenes. "The city is always interesting, but particularly interesting at 4 a.m.," Burnett said.
The show hasn't announced what night-owl celebrity guests will join them.
Burnett joked that the staffer who thought of the 4 a.m. taping has since been fired.