The Du Pont Co., the nation's largest chemical firm and one of American industry's leading holdouts against big unions, is the target of a renewed organizing drive by the United Steelworkers of America.

The focus of the stepped-up effort is Du Pont's sprawling southern phalanx, where the union is prepairing to pour in additional organizing manpower to capitalize on what it describes as a "spontaneous" display of interest on the part of unorganized workers.

Union officials concede that it may be a while, perhaps more than just months, before they can move for recognition as bargaining agent for 66,000 nonsupervisory employes at Du-Pont's 100 plants in the United States, only a few of which are represented by national unions.

But they claim more momentum now than they've had since an initial sign-up by some of the independent unions at the start of the USWA-Du-Pont organizing drive in the early 1970s.

"We were stalemated for the past year or so," said Elmer Chatak, organizing director for the 1.4-million-member USWA, the country's second-largest manufacturing union, the largest within the AFL-CIO. "But with the new surge of interest in the southern plants, we've had a substantial move forward."

Du Pont officials will neither confirm nor deny Chatak's claim. "They don't represent any Du Pont employes today and we haven't seen any evidence of card-signing," said Don Hunton, public affairs officer for the company.

Instead of card-signing efforts, the union has been concentrating on winning over independent unions that represent workers at about one-third of the plants and establishing organizing committees at the unorganized plants.

As of now, according to Chatak, the USWA has won endorsements from 17 or 31 independent blue-collar unions and has set up organizing committees at 13 or more other unorganized plants, involving a total of about 1,200 volunteer Steelworkers organizers within Du Pont.

Four of the new organizing committees were set up over the last several months at large plants in Martinsville, and Kinston, NC - the largest such Va., Richmond, Va., Wilmington, N.C., gain since the start of the campaign, according to Chatak.

"They came to us, we didn't come to them," said Chatak, who responded by moving to devote more attention to Du Pont's 26 plants in the South. Before then, the union had concentrated mainly on recruiting the six big independent unions that still resisted the Steelworkers' blandishments.

While the South, with its right-to-work laws and paternalistic approach to labor-management relations, has not been fertile turf for unions, the USWA achieved a notable break-through earlier this year in organizing the huge Newport News Shipbuilding Drydock Co., in southeastern Virginia.

The National Labor Relations Board certified the USWA last week as bargaining agent for 19,000 Newport News employes.

Similarly, the United Auto Workers, the largest industrial union, recently forced General Motors to drop its socalled "southern strategy" to keep the UAW out of its growing southern complex of plants, winning instead a preferential recruiting system that seems likely to give the auto union a powerful foothold in the South.

But the textile industry remains a symbol of big labor's continuing weakness in the South, with the huge J.P. Stevens Co. holding out against a union-led boycott of its products and the adverse publicity of periodic unfair labor practice charges.

A victory at Du Pont would be more than a regional boon, to unionism, however. Despite membership gains nationally in recent months, unions are still commanding declining share of the work force and losing at least half their representational elections. Most of the big gains have come among public employe unions, and industrial unions are beset by trade and automation problems as well as non-union competition.

Although Chatak contends that Du Pont has increased its resistance to the USWA as the union has grown in strength, the resistance has been low-key.

One of the union's problems is that Du Pont has always succeeded in coopting the big unions with relatively good wage- and benefit-levels. The USWA says in effect that it, as a union big and powerful enough to tangle with a giant like Du Pont, can get more.

Du Pont organizing drives go back many years, but the USWA campaign began shortly after the union took over the catchall District 50 of the United Mine Workers and its chemical plant targets in the early 1970s.

With a majority of workers signed up in at least 10 plants with independent unions, the Steelworkers could move now for some plant-by-plant elections. But, according to Chatak, it is waiting until it achieves a strong enough base at the 75 largest plants to seek recognition everywhere at once, in any plant where a majority can be signed up.

When - if ever - such a step may come is unclear. Chatak says even he doesn't know, but says "We're here to stay."