There's a new rental game in town, and so far the Foxchase of Alexandria is attracting tenant-players at a rate now exceeding a hundred a month.

Mayor Charles Beatley, who has lived for years in a nearby house in Seminary Hill, is unrestrainedly jubilant about the total rehabilitation of the former giant Shirley Duke low-rise apartment complex that he saw built 30 years ago and then deteriorate into what he described as a "cesspool."

A few years ago the living conditions became so bad that the buildings, which had been allowed to deteriorate by a group of owners, were denied occupancy permits and finally were foreclosed by lenders.

Then a distress sale was negotiated last year, and a group headed by Baltimore developer Morton Sarubin and Bush Construction Co. of Norfolk arranged for Virginia-subsidized construction financing and 40-year federally insured financing at below-market rates. The National Housing Partnership then was brought into the development leadership, and a massive rehabilitation program got under way.

The first completely redone apartments were ready for occupants last fall. Despite the average, but now relatively high, rent schedule -- ranging from $320 a month for a small one-bedroom unit to $510 for the largest two-story duplex with two bedrooms and 2 1/2 baths -- the apartments rented well. By January the pace was a hundred a month. One reason was the shortage of moderate-rent apartments in the area and the conversion to condominium ownership of a number of apartment buildings, mostly in the District and Montgomery County but also in Northern Virginia.

Another source of tenants came, somewhat fortuitously, from the national elections that brought a number of new representatives and their staffs to Washington. Five of the 10 staff members in the office of Rep. John LeBoutillier (R-N.Y.) wound up in Foxchase apartments, for example.

"Our administrative assistant, Christian Braunlich, came down from Long Island and looked around for rental apartments. He chose one for himself and his intended bride and recommended that the rest of us give Foxchase a look. He said it was the best for the money and that immediate occupancy was available," said Teresa Meehan, an assistant caseworker for LeBoutillier.

Now Meehan has a one-bedroom apartment. "Not much furniture yet, but I like it," she said. "It's convenient, and I feel secure. Can't wait until the grass greens up."

Edward Christ, director for grants and projects in the Long Island congressman's office, said that he and wife Mary and their baby are comfortable in a two-bedroom, two-story unit that rents for $495 a month. Utilities are paid by tenants. He said the January gas bill for heating and cooking was $50, and the electrical bill about $35.

"We anticipate using the tennis courts and pool," he added. There are a new pool and two tennis courts in each of the four neighborhoods of Foxchase. Ed Christ said that many of the new residents are young and that the congressional staffers find it both convenient and economical to carpool.

Hal Furman, a legislative assistant to Sen. Paul Laxalt (R-Nev.), came to the Washington area for the first time late last year and "looked around" before deciding to lease at Foxchase. "My wife Ann [a legal assistant in a law firm here] and I liked the idea of moving into a new apartment and being able to have bus-subway service as an alternative to driving every day," he said. The Furmans have a two-bedroom apartment.

In terms of the Foxchase and its relationship to Alexandria, Mayor Beatley expresses his approval of the massive renovation as a nearby resident in Seminary Hills. "I remember how bad it got to be before it was finally vacated and sold," he said. "It was worse than the image of the worst of public housing in cities other than Alexandria."

Beatley said that the Foxchase complex of 200 buildings, with a potential of about 5,000 residents, represents about 4 percent of all the dwellings in Alexandria.

The city has seen its proportion of rental dwellings decline from 80 percent to 50 percent in the last decade. Many new and converted condominium apartments now are part of the Alexandria housing stock. Other than the Foxchase, Alexandria's major concentrations of rental apartments are in the low-rise Hamlets and the high-rise Southern Towers and Seminary Towers near Shirley Highway.

As a source of income to the city, the rehabilitated Foxchase is likely to increase 10-fold after the work is completed and all the apartments are occupied, now targeted in mid- or late 1982 if the strong rental market continues.

Marketing consultant Robert Cagann said that about 50 percent of the new tenants are coming from Northern Virginian and the rest from elsewhere. "If the condo conversion trend continues, we will probably get more tenants from Montgomery and Prince George's counties," he added.

One of the stipulations for the federal financing obtained for Foxchase is that 20 percent of the rental dwelling be available to Section 8 tenants. Those are persons or couples eligible by income for rent subsidies. While most of the new Foxchase residents are spending 25 to 30 percent of their gross incomes for rent, the Section 8 tenants will contribute a maximum of 25 percent of income and get a federal subsidy for the difference between that and market rents.

In addition to being the area's most dramatic example of a deteriorated rental complex which has been rehabilitated for tenants instead of condominium ownership, the Foxchase also offers assurance that there will be no conversion to condo ownership for at least 20 years. "That's part of our agreement to obtain HUD-aided financing," said developer Sarubin.

Leasing consultant Cagann said that tenants are told that their rents will not be increased until rehabilitation and occupancy are completed. "Then we have to get HUD permission for any rent increase," Sarubin added.

Most of the new Foxchase residents are young, and there are few children in the relatively small apartments. However, more than 20 percent of the eventual total tenant mix is likely to be older -- many of whom will be eligible for Sectiuon 8 rental assistance.

Sarubin estimated that it would cost at least $60,000 per unit to build comparable new apartments, whereas the cost to restore each unit is about $35,000. That does not include any ground cost. The 100-acre apartment tract now would be worth, according to Sarubin, at least $7,000 to $10,000 per unit for ground. With 2,113 apartments involved, that could be as much as $20 million just for the ground. And that figure coincides with the approximate amount paid for the deteriorated complex little more than a year ago.

The site, which includes a shopping center that will be upgraded in the 4600 block of Duke Street, covers an area intersected by Jordan Avenue. Hundreds of existing trees have been saved despite the construction work, and Sarubin estimated that at least $500,000 will be spent on new landscaping.

Could a comparable rental complex be built today for moderate-income tenancy? "Not with today's land costs for a comparable location, and not without some government aid on the financing side," said Sarubin. "It's only the long-term financing at below-market rates that makes this feasible. We are allowed to make only 6 percent on our original equity contribution. Most of the investors are seeking tax shelter and hoping for long-term appreciation in value.

"Only a philanthropist could reproduce the same quality apartments at the same rents," he added.

With the rehabilitation program going along at a fast pace, including the addition of a fourth floor on some buildings to provide two-story apartments, the challenge to rent the units accelerates. "We expect to reach the level of being able to supply 150 apartments a month for the area rental market before long," said Cagann. We're right at the mid-market level in rents now. But with our original rental schedule frozen until we finish up, that means that we'll likely be 5 percent or 6 percent below market by the time we finish next summer."

Meanwhile, a major attraction for moving into Foxchase is that it is perceived as "new" by tenants who also like the convenient location. And there's also the assurance of no conversion to condo ownership before the year 2000. Seventy-five percent of the 2,113 units are one-bedroom apartmens that appeal to young single persons or couples without children.

Harold Furman said his decision to rent at Foxchase was based on affordability and location, "and I really liked the fact that we'd be the first tenants in this apartment."

There are thousands of less expensive one- and two-bedroom apartments being rented in the Washington area. But none are new, and there are infrequent vacancies in those that are regarded as highly attractive in terms of both maintenance and location.

The rejuvenation of the former Shirley Duke apartment complex is considered a double blessing by Mayor Beatley, who said that the city benefited by getting rid of a bad housing situation and coming up with an attractive, newly redone complex that provides reasonable places to live for persons who choose to rent.

If the area has an acute shortage of new rental apartments in the moderate price range, the Foxchase of Alexandria will be completely leased before the winter of 1982.