Gunmen posing as army soldiers today shot and killed the head of one of the principal Lebanese Christian clans, Dany Chamoun, and his wife and two sons at their home in East Beirut.

Mr. Chamoun, whose father was President of Lebanon from 1952 to 1958, was a close associate of Gen. Michel Aoun, the rebellious Christian military leader who was forced to surrender to the Government on Oct. 13 and has taken refuge in the French Embassy.

The general's surrender after an attack by Syrian and Lebanese Army troops was hailed by Lebanese leaders as sign that prospects were improving for a peaceful settlement of Lebanon's 15-year-old civil war. But today's killing, for which no group claimed responsibility, raised concern that a new round of violence might erupt between rival Christian factions and possibly between Christian forces and the Syrian Army.

Mr. Chamoun, 56 years old, inherited his political career and the presidency of the National Liberal Party, a rightist Christian group, from his father, Camille. As President in 1958, the elder Mr. Chamoun asked the United States to send troops to preserve his Government, which he said was threatened by an internal Muslim and leftist rebellion and a new military regime in Iraq. The Eisenhower Administration sent 10,000 marines, who stayed from July to October. The former President died in 1987. Gunmen in Camouflage

Dany Chamoun also led an armed faction of Lebanese Christians after the civil war began in 1975. He was a staunch supporter and adviser of General Aoun, who fought against the Syrian-backed Government of President Elias Hrawi.

Mr. Chamoun was also a rival to the hard-line Christian militia leader Samir Geagea, who fought General Aoun early this year for the military leadership of the Christian community, and lost.

After General Aoun's surrender, Mr. Chamoun refused to escape to an area north of Beirut held by his enemies, preferring to stay at home in the East Beirut suburb of Baabda under protection of pro-Syrian Lebanese Army soldiers, his neighbors said.

Security officials said a dozen gunmen in camouflage combat uniforms surrounded the apartment building where Mr. Chamoun lived at 7:10 this morning.

Some of them burst into his fifth-floor apartment and riddled him with bullets as soon as he answered their knock at the door. Infant Daughter Survives

Then they fired their silencer-equipped pistols and machine guns at his wife, Ingrid; their two sons, Tarek, 5, and Jerome, 7, and their 11-month-old daughter, Tamara.

The assailants fled to an unknown destination in two BMWs that had no license plates, the security officials said.

Mr. Chamoun, his wife and Tarek were killed immediately, and Jerome died at a hospital. The infant girl was wounded but survived, doctors and witnesses said.

The assassination intensified Christian anger over reports that Syrian Army troops had executed soldiers loyal to General Aoun who had confronted them during the Oct. 13 attack. At least 750 people were killed in the Syrian-led offensive and the reprisals that followed, military and hospital officials have said.

About 30 soldiers were reported to have been shot point-blank after they surrendered to the Syrians near the presidential palace in Baabda, where General Aoun had his headquarters. Prime Minister at Scene

Mr. Chamoun had escaped several assassination attempts, including one in July 1980 when gunmen led by a Christian militia leader, Bashir Gemayel, went on a rampage, killing 90 of Mr. Chamoun's followers in a drive to unify the Christian militias. Bashir Gemayel was assassinated in 1982, 22 days after Parliament elected him President of Lebanon.

Mr. Chamoun has an elder brother who preferred to leave politics and go into business in Paris. He also has a 27-year-old daughter, Tracy, who lives and works in London.

Prime Minister Selim al-Hoss was the first to visit the scene of the crime. Mr. Hoss, a Sunni Muslim, decribed the killing as "a brutal crime committed by an enemy with evil intentions against the march of reconciliation and legitimacy."

He said that during the last few weeks, Mr. Chamoun was in contact with him, expressing moderate views of openness toward the Government. "Maybe he fell a victim of this responsible attitude," Mr. Hoss said.

Mr. Hoss added that the crime would not be allowed to undermine the Government's attempt to unify the country, "a process of peace and reconciliation." Restraint Is Urged

The Druse leader Walid Jumblatt lashed out against the Government for negligence and accused the Lebanese Ambassador in Paris, Johnny Abdo, of conspiring with Mr. Geagea in the planning of the assassination. Mr. Geagea condemned the killing.

President Hrawi, visiting Syria, called his headquarters in East Beirut and expressed sorrow and regret over the incident, official sources said.

He urged "all to exercise maximum self-restraint and not get carried away by schemes which aim at restoring the atmosphere of tension in the country."

Lebanese and Syrian forces today stormed homes and set up roadblocks in a bid to arrest the killers of Mr. Chamoun. Syria has 40,000 troops in Lebanon; their refusal to say when they would leave the country under a peace accord signed last year in Saudi Arabia was one of the principal reasons General Aoun gave for the military opposition he led for 11 months before his surrender.

Mr. Hrawi's Government accepts Syria's promise to depart eventually. The peace accord provides for a new formula for power sharing among the religious groups in the country, ending the Christian dominance of the Government and increasing the Muslims' power.

Photo: The body of Dany Chamoun, the head of one of the principal Lebanese Christian clans, on the floor of his Beirut home. He, his wife and his two sons were slain yesterday by gunmen posing as army soldiers. (Agence France-Presse)