THE REPUBLICANS welcomed a racist last week and termed the occasion an indication of their popular appeal.

Eddie Vrdolyak, former boss of Chicago, announced he was leaving the Democratic party of his immigrant parents, who found a home in one of the ethnic neighborhoods of Chicago, in order to join the Republican party of Lake Shore Drive. Apparently the Democrats no longer represented the interests that had drawn Vrdolyak's family to the party.

To Vrdolyak those interests are tied to supporting the white ethnic workers upon whose votes the urban political machine originally had been based. To its credit, the Democratic party no longer represents only the interests of this group of white people. It has in recent years recognized the Blacks that live in the city.

FORTUNATELY for the party the needs of white ethnic and Black laborers are very similiar. Vrdolyak has refused to recognize that. Instead he has let his own distaste for dealing with Black politicians drive him from the party that strives to meet the needs of all people.

The only interest the Democrats are not meeting is the personal ambition of Vrdolyak. The former leader of the Cook County Democratic machine could not win the party's endorsement for mayor--and he couldn't garner enough votes as a third party candidate to unseat incumbent Democrat Harold Washington.

When Washington, the first Black Mayor of Chicago, first won the nomination of the party five years ago, Vrdolyak, who was a chief alderman, embarked on a political battle with his party colleague. Vrdolyak, the son of a Lithuanian saloon keeper, refused to share power on equal terms with the Blacks in the city.

The battle between the two--dubbed council wars by local comics who portrayed Vrdolyak as a Darth Vader and Washington as a Luke Skywalker who destroyed the "machine star" by hitting at its core, the mayor's office--had its final clash this past year when Washington showed that he had enough political clout to maintain his Democratic endorsement for Mayor. He then handily won the general election, defeating a Republican and Vrdolyak.

THE ELECTION proved that Chicago politics had been changed for ever. Blacks, not Irish or Slavs, are now the dominant ethnic force. But this is not the Chicago machine's last hurrah; it's a chance for a new beginning.

The Cook County machine is one of the most famous in the nation. It was in Cook County that John F. Kennedy received the votes to take the state of Illinois from Richard M. Nixon. At the time the machine was run by the famed Richard Daley.

Vrdolyak was Daley's successor but he failed to learn one of the principal lessons of the machine politician: every vote--no matter who casts it--counts toward victory.

Vrdolyak didn't want the votes of Blacks. Daley never had to confront his prejudice because in his time the Black vote was still disenfranchised. But while Daley never dealt with the Black vote; Vrdolyak did--and this latter day boss did not adapt to let Blacks into the machine on an equal level.

Even in Daley's time there was powersharing between different ethnic groups--the Irish, Italians, Slavs, Poles and Jews. Now that Blacks have joined that group of powerful voting ethnic groups there is an opportunity to over-come national race divisions in America's great melting pot--the city.

A new situation exists in Chicago. A Black man clearly is at the head of the Democratic Party in Chicago. The question is whether the old machine style of powersharing between different ethnic voting blocks will work to keep the city at political peace or whether age-old racial divisions will prove too strong. Will racial prejudice in ethnic neighborhoods--spurred on by the baiting rhetoric of people like Vrdolyak who has begun to reach for the Republicans in neighborhoods he used to wardheel as a Democrat--make a white-Black sharing of power impossible as long as the Blacks are dominant?

The answer to this question not only will influence the political future of the city but also will be a telling sign for all of America, where unfortunately racial divisions have become more noticeable in recent years. Vrdolyak's response is not a promising omen for the American future. Hopefully other white politicians will learn to accept Blacks on equal terms.