A railroad boxcar-making factory in Alexandria, an old roundhouse in Hagerstown and O. Roy Chalk, former owner of the Washington bus system, are among the contestants in a spirited behind-the-scenes competition for a lucrative prize to be awarded this summer: the contract to assemble 294 Metro subway cars being built in Italy.

Maryland, Virginia nad the District of Columbia are partners in development of the subway system but furious rivals in the competition to land a contract that means jobs, money and perhaps a long-term partnership with a major international industrial corporation.

The subway cars, to be delivered beginning next year, are being manufactureed by Breda Costruzioni Ferroviare of Florence, at a cost of more than $800,000 each. Because the federal government is paying much of the cost, U.S. law requires that they be assembled in this country. Breda executives were in the U.S. last month trying to decide where to do the work. e

Among the leading possibilities are the boxcar-manufacturing plant of Fruit Growers Express Inc. in Alexandria (which has the advantage of being adjacent to the Metro tracks), an underused Chessie roundhouse in Hagerstown and rail facilities in Philadelphia and New York. In addition, the District government's Office of Business and Economic Development is trying to persuade Breda to select a contractor who would do the work in the District.

The last meeting the Breda executives had before returning to Italy was with Chalk, who owned the old D.C. Transit bus system until it was taken over by Metro. Paulo Longo, Breda's representative in New York, confirmed that Chalk had "expressed an interest in the project and we gave him our list of specifications," but he would not say whether Chalk had made specific proposals.Chalk declined to comment.

The cars Metro is operating now were manufactured in the U.S. by a company that is no longer in the mass-transit business. Forced to find a new supplier for cars it must have to open the remainder of the rail system, Metro awarded the contract to Breda. The first 94 cars are due to be delivered for testing about 11 months from now. The other 200 are to be delivered in increments beginning in 1983, ensuring the assembly subcontractor several years' work.

General Manager Richard Page and other Metro officials said they do not know which contractor Breda will select, and while they would prefer to see the work done in the Washington area they have no control over it.

According to Dennis Murphy, industrial development representative in the Maryland Department of Economic and Community Development, who has spent two years trying to secure the contract for Maryland, more is at stake than the immediate work of assembling the cars and adding the propulsion systems and air conditioning compressors.

He said Breda, which is also supplying new rapid transit cars to Cleveland, "is becoming a force in this business. They are in the marketplace and may be supplying cars for other systems. Also, Breda is part of an industrial group that makes trucks, buses and helicopters. They are a major company that could want a long-term relationship."

Lawrence Schumake, economic development director for the District, said that "it's not that big a contract in the number of jobs, but we would have to look at spinoff jobs, long-term potential and long-term maintenance." He said that "at least two" proposals have been submitted to Breda by contractors who would do the work in the District.

The Virginia candidate, Fruit Growers Express, jointly owned by several railroads, operates a 50-year-old boxcar-manufacturing plant on Roth Street in Alexandria that the Italians reportedly have said is outmoded. Walter Dahl, Fruit Growers' vice president for marketing, said, "We met with the Breda people and we told them, we have the space, the personnel, the interest and the location. But we don't know yet if we are going to bid on the contract. Is it feasible for us?" If it required construction of a new plant, he said, it might not be profitable for his company to undertake it.

Maryland's leading entry appears to be the Chessie System roundhouse at the railroad yards in Hagerstown, a Western Maryland community with a high unemployment rate.