Work has begun on a complex in the heart of Georgetown that will include rental apartments, retail shops and office space around a central courtyard.

The project, called Prospect Place, is located behind the Billy Martin restaurants, with frontage on Prospect Avenue and N Street. The complex will include 35 apartments and duplexes of various sizes, plus 37,000 square feet of retail space and offices. Construction on the 52,000-square-foot site will be brick with metal roofs.

The property formerly contained the Chestnut Farms Dairy, owned by Craft Inc. The developer of the $10 million project will be Phenix-Georgetown, Inc., of which Charles K. Greenwald is executive vice president.

Greenwald said yesterday that the Prospect Place plan has received the approval of the Fine Arts Commission and needs no zoning changes to conform with the existing C-2-A category for commercial use and height ceiling of 60 feet. He estimated the value of the undeveloped site at $30 a square foot.

Architect Philip E. Tobey, a partner in Metcalf and Associates and project manager for Prospect Place, said the Metcalf firm and realtor Jeanne F. Beggs, whose firm will handle leasing and management, advanced the idea of including rental apartments because of professional and personal convictions that total quality of Georgetown life would be enhanced by persons living in "excitingly designed, high-rent dwellings over the stores."

Although Kraft, Inc., as the landowner and major stockholder, has a strong financial position in Prospect Place, Mrs. Begg and architect William H. Metcalf are stockholders. Long active on the Georgetown real estate scene, Mrs. Begg said she became interested in the former dairy site years ago when she unsuccessful presented a purchasing contract for another client to Kraft, which is a successor to National Daries, Inc., as owner of the tract originally aquired in 1923.

"Then I met architect Bill Metcalf at a party and discussed the site," she said. "We agreed that its redevelopment would be exciting for the area of Georgetown north of M Street. We also decided that our ideas should be formally proposed to the site owner. So, after many years, this multi-use development is getting under way.

The Chase. H. Tompkins Co. of Washington will be the general contractor. Landscaping, including some large new trees, will be done by Lester Collins.

Architect Tobey pointed out that the two primarily residential buildings will front on Prospect Avenue, which is 10 feet lower than N Street, where the office building will be located. In between, a sunken, masonry-faced courtyard with two small commercial buildings, as anchors, will be connected by an overhead trellis. The eastern boundary of the site borders a 10-foot alley between Prospect and N, against which another row of shops will back and fore the courtyard.

Tobey said the building plans already have been submitted to the D.C. government and are expected to be approved so that the foundation work can be started in November.

There will be entrances on both Prospect Avenue and N Street and underground parking for 117 cars, with the access on Prospect.

Planning and engineering for the project have been under way since April, 1975. Construction financing has been committed by Manufactueres Hanover Trust Co. of New York, according to Greenwald, and Western Savings Bank of Philadelphia will provide the permanent loan.

Mrs. Begg said that the 37,000 total of retail square feet will be competitively priced in the "boutique range" and that the 13,000 square feet of office space will be about $10.50 a square foot. Both the Begg and Metcalf firms may take some of that space.

Retail space is programmed to be ready before Dec. 1, 1978, and apartments ready for occupancy early in 1979. CAPTION: Picture 1, Workmen clear the Georgetown site where Prospect Plaza will be built. By Vanessa R. Barnes - The Washington Post; Picture 2, Drawing shows the $10 million complex between N and Prospect Streets.