It is an axiom of the turbulent, bloody history of farm labor conflict in the southwest that unions rarely win a strike near the border and its cheap, plentiful supply of Mexican labor.

That axiom appears to have gone the way of the 19-cent head of lettuce after a carefully designed walkout that United Farm Workers President Cesar Chavez calls "a dream strike" because of its virtual absence of strike breakers.It is a dream that growers say will become a nightmare for American consumers if Chavez's demands are met.

As the sometimes-violent Imperial Valley strike enters its third week, the eight struck growers who produce nearly a third of the nation's winter (iceberg) lettuce have been unable to find a surplus Mexican labor force, either legal or illegal, to harvest the crop now rotting in the fields.

"No Mexican farm worker in his right mind is going to break the strike," Chavez said late last week in an interview at his Tehachapi Mountains headquarters 350 miles north of the struck lettuce fields. "It's just impossible."

As the growers see it, this "impossibility" is partly the result of a campaign of intimidation of Mexican workers by the UFW, which has advertised in Mexican newspapers in support of the strike. The union, in turn, accuses growers of encouraging "racism" by emphasizing the Mexican nationality of the workers and by conspicuously recruiting Anglo high school students as volunteers to help in the harvest.

In the tumultuous strikes of the 1930s, when Imperial County boasted of being "the cradle of vigilantism," a series of farm walkouts was broken by the arrest of strikers, vigilante violence and importation of strikebreakers.

That era is over now, and a new era -- one that might be called the era of agricultural industrial unionism -- has come to California. It is an era when the police are evenhanded and when Mexicans are no longer willing to undercut the union to salvage the harvest.

"Only if the workers break ranks," says Chavez, who doesn't think this is going to happen, "can the growers win this strike."

Most of the strikers are Mexican residents, so-called "green carders" who cross over the border each day using legal work permits. The growers, who depend on this labor supply and resent its new-found militance, point out that these border-crossing field-hands earn far more each day than they could make in Mexico.

Whether because of union solidarity, intimidation or the heroic image which Chavez holds for many of Mexican descent on both sides of the border, both sides agree that racial tensions are increasing and very few Mexicans now are willing to work in the fields.

They also agree that the practical result of a "Volunteer Harvest Day" that the growers staged last week was insignificant except as a symbolic event. Bill Roberts, a Southern California political consultant the growers have hired as a publicist, estimates that not more than 5 percent of the crop can be brought in by volunteers.

Referring to the volunteers who helped bring in the crop last week, UFW publicist Marc Grossman said: "They were mainly children and women and old people. The ladies' bridge club of Pasadena could do a better job of picking lettuce."

Before the strike is over, the economic impact on both sides -- and on consumers throughout the nation -- promises to be very great, and not only on lettuce prices.

The Imperial Valley, where only eight of the 28 lettuce producers have been struck, produces 95 percent of the nation's winter iceburg lettuce crop. But is also produces substantial amounts of celery, asparagus, melons and tomatoes and the planting of these crops has been disrupted.

Furthermore, the strike is considered certain to spread. Already the walkout has spilled over to the rich Salinas Valley in Northern California, where a few of the struck Imperial Valley growers have operations that have been shut down.

Chavez said in his interview that he views the lettuce strike as part of an overall strategy that will "bridge some of the disparities between farm workers and other workers."

Always before, said Chavez, the United Farm Workers fought simply for survival -- first, against the grape growers of California's San Joaquin Valley and then against the Teamsters. But the passage of a California law that ensured collective bargaining in agriculture and a subsequent jurisdictional agreement between the UFW and the Teamsters have given Chavez's union new bargaining muscle.

Now, Chavez thinks of the UFW as a union that can behave like an industrial labor union and bargain effectively for major economic benefits for its members. This conception was reflected in the UFW's first contract proposal, which asked for an increase of the basic minimum wage from $3.70 an hour to $5.25. The struck growers countered with a 7 percent offer -- 26 cents an hour -- which they said complied with President Carter's wage guidelines.

Jon Vessey, the second grower struck in the Imperial Valley, says that 80 percent of the workers are on piece rates and earn between $8 and $12 an hour. Caridad Sanchez, a labor market analyst for the state, says that the average is never less than $6 or $7 an hour.

However, Sanchez adds that about one half of the workers drop below the $4-an-hour level in pre-harvest periods. Carter's wage guidelines are supposed to apply to workers earning $4 an hour or more.

Under the contract sought by Chavez, a lettuce loader who now makes as much as $89 a day (excluding medical benefits) would make $220 a day. Lettuce crew members who get the piece rate of 57 cents per 24-head box would get 87 cents a box.

(A check of several Washington-area grocery stores today showed that most were selling iceberg lettuce for 79 cents a head, a price that jumped from 49 to 59 cents a head a month ago.)

The growers, fearing a long strike have asked for federal mediation. Chavez, aware that he has more economic power now than he is likely to have later, has rejected mediation.

By striking selected targets at a time when lettuce prices are high, Chavez has tried to encourage the growers, who can see their competitors making huge profits, to make a quick and generous settlement. He hopes to use this prospective settlement as leverage for other contracts.

The question is whether Chavez miscalculated and struck too soon. The UFW pays only $25 a week in strike benefits, and no payments were made during the first two weeks of the walkout. Some doubt that the farm workers will be able to hold out during a long strike, and the growers hope that their increasing desperation will turn them away from Chavez.

"We feel that there is a silent majority of workers out there who believe that their union is being unreasonable," says Vessey. "And the growers are united because this contract would affect all the produce in the state of California. We'll never sign this, I'll guarantee you that."

With growers and the union far apart, the only harvest reaped so far by the strike has been one of bitterness and violence.

A clash last Monday left two strikers in the hospital and caused the smashing of several vehicles owned by the growers.

Imperial County Sheriff's Lt. Richard Wilson says that the violence apparently was started by private security guards hired by some growers. He adds that his department also is investigating allegations that a striker set a grower's truck on fire and that a 64-year-old man was knocked unconscious when a picket hurled a rock through his windshield.