St. Louis — Chris McNairy walked into the Jesse Jackson headquarters the other day and offered to be a campaign volunteer. ''He's building on something,'' said Mr. McNairy, who last year became the first black student-body president at Washington University. ''As far as rainbow coalitions and all this, it's more than dreams. I see that because I'm living proof of it.''
One day, he says, he wants to be a politician.
McNairy's aspirations are a hint that something is stirring in black America. In increasing numbers blacks are registering to vote. They are electing black leaders to positions once the reserve of whites. And they are boosting in a dramatic way Mr. Jackson's bid for the Democratic presidential nomination.
(Preliminary results from Wednesday's Missouri caucuses gave Jackson seven delegates to the party's national convention in July, compared to Walter Mondale's 50 and Gary Hart's 18.)
Despite his low delegate count in the primaries so far, Jackson's campaign is expected to have an impact long after the 1984 race.
''Politics,'' says Paul M. Green, ''has become a second religion in the black community.'' Mr. Green is director of the Institute for Public Policy and Administration at Governors State University in Chicago. He notes that the black political movement definitely predates the Jackson campaign.
According to the Joint Center for Political Studies, the number of black officials rose 8.6 percent from 1982 to '83, after several years of more meager increases. Last year, Chicago and Philadelphia elected their first black mayors.
What Jackson has done is to capitalize on and dramatically expand that movement, says Lucius Barker, chairman of the political science department at the University of Missouri at St. Louis.
The Atlanta-based Voter Education Project reports that in registration, seven southern states have added 407,000 black voters since the 1982 congressional elections. Significantly, these figures reflect the routine subtraction of voters as names and addresses are verified, says a project official. ''Even to maintain black registration levels requires active work.''
In vote-getting, however, Jackson's success has surprised some people.
In December, soon after he formally entered the race, he was expected at best to win 50 to 60 percent of the black vote, says Lorn S. Foster, senior fellow at the Joint Center. Instead, he has racked up 77 percent of the black vote in Pennsylvania, 79 percent in Illinois, and 87 percent in New York.
Here in St. Louis, Jackson's strength has been evident.
''It has not been any problem to get our black people and right-thinking white people to support Reverend Jackson,'' said Charles L. Bussey Jr., state campaign chairman for Jackson, interviewed shortly before the caucuses. ''The only question has been: How do you get the leaders?''
When Mr. Bussey talked to several local black officials four months ago, they ''thought Jackson's campaign was quixotic,'' he says. Now, 90 percent openly endorse him; most of the uncommitted are also leaning toward him, he adds.
''This is a campaign that has transcended institutional politics,'' bringing together established leaders, the clergy, disaffected voters, and other segments of the black community, Mr. Foster says.
The black vote ''is going to have to be played very carefully'' by the Democratic Party, agrees George Wendel, director of the Center for Urban Programs at St. Louis University.
One dilemma is Jackson's demand for the elimination of runoff primaries in the South.
If the eventual Democratic nominee doesn't go along, he risks losing the support of Jackson and, perhaps, many blacks. If he accepts, he risks the wrath of southern white Democrats.
Given its relatively small size, the black vote ''is always going to be a selective strength,'' Mr. Wendel cautions. But it will have a great impact in cities with large black populations.
Blacks in St. Louis, who make up 46 percent of the population, are showing uncharacteristic unity in the Jackson campaign, observers say.
A final legacy of the Jackson campaign: He has opened doors for future black candidates.
''Let me tell you: (Jackson's) not going to retire,'' Bussey hastens to add. But even if he does, a new crop of younger blacks could well take up the mantle.
Young McNairy, for example, who asks that his words be attributed by name, seems to be learning his political lessons early.