ONE DAY in New York City several months ago, Peter Jablow, executive director of Washington's Cultural Alliance, was walking down the street with Hugh Southern, the man who put together TKTS, the successful Times Square box office that sells same-day discount tickets for some of New York's best theaters.

They were not far from the TKTS trailer on 46th Street where an irate woman approached Southern and complained about the long line outside the box office. "I'm tired of this! I'm going off to the theater and buy the full-price ticket!" she exclaimed and marched off.

Southern turned to Jablow and said, "Successs!"

That is exactly what Jablow and a group of local theater officals want to say next spring if the Cultural Alliance -- the three-year-old umbrella service organization for 225 local arts groups and many individual artists -- succeeds in opening its own version of the central box office in Farragut Square.

The local version will be a brightly colored converted trailer -- obtained from Montgomery County -- equipped with windows, plastered with promotional posters, and topped with a long sign carrying the name "TICKETplace."

The Alliance, which has been considering the project for months, announced its final plans at a meeting last Wednesday. The group still needs approval from the District Department of Transportation for the proposed site on the 17th Street side of Farragut Square. The Alliance also needs $250,000 in start-up funds. Jablow says that some of the money has already been raised, and is confident of raising the rest from local foundations and corporations.

According to a study done here over the summer by the Theater Development Fund -- which operates the New York central box office -- there are 4.3 million tickets for performing arts events available every year in the Washington area.But 1.2 million -- 27 percent -- go unsold.

"That's why we're doing this," said Jablow. "We estimate we can sell 10 percent of the unsold tickets our first year in business if we can get the booth in Farragut Square."

The box office will offer same-day and advance tickets to a variety of performances by both large and small groups. On the day of performance, all tickets will be half-price. "There are producers of shows who have seen empty seats the night of performances," said David Anderson, manager of the Warner Theater. "I think they would rather see prices go for half as opposed to unsold."

The office -- which cannot support itself without service charges -- will charge 50 cents on every half-price ticket under $10 and $1 on every half-price ticket $10 and over. There will be no service charge on full-price advance sale tickets.

"It will take about six months to catch on," said Alex Morr, the theater consultant who headed the Alliance's task force on TICKETplace. Each theater will be able to choose whether or not it wants to allocate tickets for certain shows on certain days. "There's no way they won't go with something that sells," Morr said.

The TICKETplace strategy: Make it inconvenient. The box-office manager will make sure there's a line at the booth. No phone orders. No credit cards. Cash only.

"You're standing in line, cash in hand," said Jablow. "If you get up to the window and the show you came to buy tickets for is sold out, you'll buy something else. If you didn't like what you tried, you won't go again. But if you did, you'll come back."

The consumer benefits: Half-price tickets to a show that partons might not otherwise be able to afford. "'Amadeus' at $25 is one thing," said one local theater manager. "But at $12.50, it's another."

Benefits for the theaters: "Crossfertilization," said Jablow, meaning that patrons would end up at performances they might never have visited.

Another benefit: New audiences. We're looking forward to doubling some of our concerts -- if not all of them," said Barbara Serage, managing director of the Fairfax Symphony and a Cultural Alliance member. "Considering where we are in our growth, it sounds like it will be a real boon to us."

"We're looking for the creation of the secondary market," said Morr. "It's people who can't afford buying full-price tickets frequently. And it's young people who don't want to be tied down to an advance time. If you have a centralized facility and they're determined to see something tonight, they'll buy something that isn't necessarily their first choice."

Eventually, the reasoning goes, these people get more interested in theater. They also become older, more affluent, and less patient with standing in line. "In New York, the age-bracket of central box-office goers has remained the same over the years," said Morr. "So that means people graduated to full-price reserved ticket buyers."

Both large and small performing arts groups support the idea, including the Kennedy Center, National Symphony, Folger Theater, Arena Stage and the Warner and National theaters.

But will the big theaters really be willing to offer advance tickets and half-price tickets? Morr estimates that 12 to 18 will be involved after about six months, and stresses that the arrangement has worked successfully in New York. The big houses are crucial: "There isn't enough variety without the large theaters," said Morr. "When you've got the headliners, it helps to draw people in -- even if they don't get to see the headliners."

But the Kennedy Center has qualms about half-price ticketing. "I know there's great reluctance on the part of the Kennedy Center," said Morr. "Some of their reasons are valid. Some of their reasons are just that they haven't tried it. I think they're being very good just cooperating."

The Center has agreed to participate in the the advance-sales part of TICKETplace, according to Richard Owens, associate manager of theaters at the Center and a member of the Alliance's task force.But as for half-price ticketing. Owens said, "That's still being discussed. I think the central box office is a terrific idea. The Kennedy Center is very supportive."

According to the Theater Development survey, of all performances at the Kennedy Center during the 1979-1980 season, 1,869,862 tickets were available -- and 395,843 went unsold.

The Warner's Anderson -- who is about to become a member of the Cultural Alliance -- said the Warner will participate "on a show-by-show basis. It will depend on what the producer wants to do. I would imagine most would have no problems with advance sales -- unless the Alliances made it difficult for us. If they decided they weren't going to pay us [the ticket revenues] very often -- say, every four weeks -- that would make it difficult. But basically we just want to make it easier to sell tickets."

National Symphony head Martin Feinstein -- a member of the Alliance task force -- said, "Not only will we allot tickets for full-price sale at the ticket booth, but if there are any available on the day of performance, we'll put them at half-price."

The Cultural Alliance has met several times in the last few months with the National Park Service and the D.C. Department of Transportation regarding the Farragut Square site. "We think it's an excellent idea," said George Berklacy, a Park Service spokesman who attended one of the meetings.

But "The District had a lot of questions about the location," said Berklacy. "Jim Clark [acting director of the District Department of Transportation] didn't give any assurance that it could be done there." Clark could not be reached for comment late last week.

The Alliance's Jablow admits that the District sees problems with the site: "Clark told us the department would have to do a traffic analysis." Jablow expects that to be done in late January.

But if the Farragut Square location is not approved, Jablow said, "We'll just look for another place."