DAVID Letterman. Late Night. Top Ten. Home Office. Paul Schaffer. Jay Leno. Lee Atwater. Chris Elliott...

Lee Atwater?

If you're asking what he's got to do with David Letterman, you're not alone. Neither are the thousands who watched their T.V.s in amazement as the recently-appointed chair of the Republican National Committee played guitar with Schaffer's Late Night Band earlier this week.

Letterman used the occasion to get a cheap laugh. "Take a look at the band," he told the audience. "Now you tell me which one's the Republican." That wasn't too hard, given that Atwater was the only one wearing a three-piece, navy blue suit.

OBVIOUSLY, Atwater wasn't on the show just so Letterman could poke fun at him. So just what was Atwater doing on Late Night?

The question's really not as perplexing as it sounds. The key to the answer? Three easy steps:

1. Recall Atwater's love for Black music, especially rhythm-and-blues.

2. Remember the Republicans' desperate desire to break the Democrats' choke hold on the Black vote.

3. Mix 1 & 2 together and see what you get.

During his widely publicized campaign to attract Blacks to the Republican Party, Atwater has been trying to gain the Black community's trust. Part of his offensive has been rhetorical. "We [the Republican Party] have a good message--a message of equal opportunity and strong values that are shared by all Americans," Atwater wrote in the Washington Post last week.

On other fronts Atwater has made his campaign a personal crusade. He's been hustling around Washington playing his guitar at rhythm-and-blues clubs, and he participated in a joint concert with Black blues singer B.B. King. And, yes, he's appeared on David Letterman.

If nothing else, Atwater's efforts to show that he can sympathize with Black concerns and lifestyles have created a stir in the national media. Pictures of the chairman strumming away have occasionally shown up on front pages ever since the November election.

BUT the media glare will mean little unless Atwater can show the Black community that he's really offering it something worth a second look. So far, events have shown that Atwater hasn't been too convincing.

Last week's massive student protest at Howard University against Atwater's appointment to the school's board of trustees--and Atwater's subsequent resignation--was a great setback for the former aide to both Senator Strom Thurmond (R.-S.C.), a one-time segregationist, and President Reagan.

Howard's decision this January to put Atwater on the board of the preeminent Black unviersity represented a Republican coup. From such a position, the former Bush campaign manager could have greatly expanded his ties to and planted seeds of mutual trust in the Black community.