The Phillips Collection has received a $500,000 challenge grant from the National Endowment for the Arts which requires an ambitious match of $1.5 million in private funds raised over three years, the NEA announced yesterday.

It is the third-largest challenge grant awarded this fiscal year by the NEA. The Dance Theatre of Harlem received an $800,000 grant. The American Film Institute received a $750,000 grant for renovation of the institute's new conservatory in Los Angeles. The San Antonio Museum Association -- which operates three San Antonio museums -- will also receive a $500,000 grant.

The Phillips will use the grant to build up its endowment, which in turn will allow the modern-art museum to raise salary levels, install a climate-control system and work on restoration of paintings. "Little if any of the money would be used for new acquisitions," said Phillips board member E. Taylor Chewning Jr. "It will be used to preserve what we have."

The grant will be not only a needed financial injection but also, the museum hopes, a catalyst for private fund-raising -- a tough job in this city and one the Phillips had never had to do in its early days.

The museum, which is known for its French Impressionist collection and owns the famous Renoir "Luncheon of the Boating Party" -- now on tour to raise funds -- was opened in 1921 by Duncan Phillips, collector and art connoisseur. The museum is housed in Duncan Phillips' home, an elegant red brick building on 21st Street near Dupont Circle. His son, Laughlin Phillips, the director of the museum, has a comfortable carpeted office on the top floor, complete with a resident white cat. When Phillips died in 1966, he left the museum a $3 million endowment.

"It hasn't grown," said Laughlin Phillips. "When my father died, the income covered 85 percent of our budget. Now it's gone way down. It covers 30 to 35 percent." With a budget of about $500,000 a year, the museum has run a deficit of $150,000 for the last four to five years. One avenue for funds -- charging admission -- has been ruled out because the city's largest museums, which are government-supported, have free entry.

Two years ago, the Phillips launched a capital funds drive with a goal of $5 million and last year began an 18-month traveling exhibition to make itself better known. "Connoisseurs seem to know us," said Phillips, "but the public doesn't."

The museum also formed a "Council of the Phillips Collection," a group of Washington notables to advise and help raise funds. Laughlin Phillips also has begun expanding his board of trustees (which for years consisted of himself, his mother, his wife, his cousin and art history professor Law Watkins, whose father was an assistant to Duncan Phillips.)

However, raising $1.5 million to match NEA's challenge grant will be a challenge. "We do have a long road ahead," said Phillips. "We'll be looking for six-figure gifts."

Some crucial wining and dining will occur. The Phillips is hosting a dinner Oct. 7 in honor of the French ambassador to open its exhibition of work by Georges Braque. "Nobody is asked to pay anything," said Phillips, "but there is some cultivation." Another dinner is scheduled for Feb. 10, 1983, cochaired by Carolyn Deaver (wife of the White House deputy chief of staff) and Union Pacific Corp. chairman James H. Evans, for new corporate members of the Phillips Collection.

Museum officials hope its new membership program will shore up substantial financial support. Individuals become members with a contribution of $1,500 to $3,000. Corporations must contribute $2,500 to $5,000.

Whatever the financial turn of events, the Phillips does not want to take refuge under the wing of the federal government. "We're very anxious not to do that," said Phillips. "My father was a real independent. To lose that identity and become part of the government would have been really horrifying to him."