The operation is being overseen by a team from the Organization for the Prohibition of Chemical Weapons (OPCW).
The mission was established under a United Nations resolution, which was passed after agreement between Russia and the US.
The resolution followed international outrage at a chemical weapons attack near Damascus in August.
In an interim report, UN chemical weapons inspectors confirmed that the nerve agent sarin had been used in the attack in Ghouta on the outskirts of the city on August 21.
It was estimated to have killed hundreds of people and was blamed by the United States and other Western powers on the regime of Bashar al-Assad. But he accuses Syrian rebels of being behind it.
“Today is the first day of destruction, in which heavy vehicles are going to run over and thus destroy missile warheads, aerial chemical bombs and mobile and static mixing and filling units,” a source with the inspection operation told the French AFP news agency.
It is not clear at which of the chemical weapons sites declared by the government, thought to number about 20, that Sunday’s operation is taking place.
The destruction of the stockpile, being carried out by the Syrians, is not expected to be straightforward, as some sites are in combat zones.
It is the first time the OPCW – based in The Hague – has been asked to oversee the destruction of a chemical weapons armory during a conflict.
The Syrian government gave details of its chemical weapons arsenal last month to the OPCW under the Russia-US agreement which also provided for Damascus to join the Chemical Weapons Convention.
That arsenal is thought to include more than 1,000 tonnes of sarin and the blister agent sulphur mustard among other banned chemicals.
Under the terms of the agreement between the US and Russia Syria’s chemical weapons capability should be removed by the middle of 2014.
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