Pat Koczur says she has a no-cost cure for the illness confronting her Oakton neighborhood, a remedy that would reduce vandalism, bolster community spirit and increase property values.

Her solution: build a private swimming and tennis club on 13 acres of vacant land in the subdivision.

The only problem is she doesn't own the land -- the Fairfax County Park Authority does.

As a result, what might have been a simple transaction has erupted into a bitter neighborhood squabble over public versus private land ownership, illustrating the web of bureaucracy that can entrap undeveloped land in rapidly developing Fairfax County.

Just the mere suggestion that the county ought to give away the land, once planned for an elementary school, has angered many neighborhood residents. Don C. Hart, a lifelong area resident, thinks it's absurd that the county should even entertain that idea. "I don't mind them (the residents) paying for the land," he says. "What burns me is this pie in the sky stuff -- trying to get something for nothing."

Koczur, Hart and several hundred others from the Clarke's Landing subdivision met last week with county officials to discuss the issue. The outcome was hardly progress.

Supporters of the private club, well organized for the meeting, held a clear majority, but opponents did not hesitate to shout them down.

The supporters took the offense, then offered to compromise. They said they wanted only 4 1/2 acres of the land. While they said they would prefer the county to give it to them, a 99-year lease would be fine. As a last resort, they would consider purchasing the plot.

"I represent the Vale Swim and Tennis Club Committee," Koczur began politely as she fiddled with the microphone in the crowded Flint Hill Elementary School cafeteria. Koczur then delivered a series of arguments designed to convince the most ardent champions of public ownership that they, too, would benefit from a private club. "For one thing it's important in an area where people move around a lot, to feel like they belong to a community. And . . . because many people are here for only a few years, it is important that we are constantly maximizing our home values."

Don Fisher, a neighbor, disagreed. "I'm not opposed to the pool," he said later. "I am opposed to turning over public land for a private club."

And Hart took issue with many of the committee arguments -- especially the mobility issue."You implied you're all transients . . ." Hart shouted from the back of the cafeteria. "Why the 99-year lease for a bunch of transients?"

So it went most of the two-hour meeting.

One by one the would-be swimmers took turns relating the history of the 13 acres and arguing that the land was rightfully theirs. They said the developer was forced to turn over the land to the county three years ago for a possible school site in return for having Clark's Landing rezoned for more intense -- and potentially more lucrative -- development.

"The people in Clarke's Landing paid for that land, the developer didn't give anything away," insists Koczur.

That's probably true," Fisher reluctantly agreed. "But technically he did give it to the county . . . what we're talking about now is a huge precedent being set."

Park Authority Assistant Director Louis Cable, who says the county has 15 to 20 similar sites, shocked the crowd when he told them park officials would have to declare the land surplus and then offer it to other county agencies before giving the land to private citizens. That presented a rather traumatic prospect to the homeowners.

"If the Park Authority declares it surplus then we really have a problem," warns Fisher, whose land is adjacent to the site. "I don't mind the Park Authority putting in ball fields, but we could end up with almost anything there -- public housing, a drug abuse center or a correctional center."

But Koczur and others say there are ways around declaring the land surplus, and they say they are not giving up.

"When you hear of private citizens asking for public land it has a very bad ring to it," Koczur concedes. But she says the subdivision, which is between Reston and Oakton, needs the club. "The nearest anything is (is) 3 1/2 miles away and that's a Giant (grocery).

"There is nothing here for the kids to do . . . and we do seem to have a lot of vandalism -- mostly smashed mailboxes," Koczur says.

County Board Vice Chairman Martha V. Pennino, who arranged the meeting at Flint Hill, says she hasn't yet taken sides in the debate. Before she makes a decision, she says she plans to read all letters and petitions (which carry a reported 398 signatures) on the issue. She then will forward the correspondence to the Park Authority, which will have to decide what, if anything, to do with the land.

Park officials refuse to speculate on the chances that 300 Clarke's Landing families may be bobbing around in a private pool next summer, but they are quick to recall some recent cases.

"We've had groups come to us before asking for Park Authority ground for various uses," says Cable, who, has been with the authority eight years. "In those instances where exclusive use was a factor, we did not decide favorably."

Furthermore, the authority has plans to seek bond monies in a 1983 referendum to turn the vacant land into a neighborhood park. But the plans, notes Cable, don't include a swimming pool.