The government has vehemently denied claims it has used chemical agents.
The US has warned that such a development would be a “red line” for possible intervention.
However, President Barack Obama has said the current intelligence on possible chemical weapon usage did not constitute sufficient proof.
On 29 April, Saraqeb, a town south-west of Aleppo, came under artillery bombardment from government positions.
Doctors at the local hospital told the BBC’s Ian Pannell they had admitted eight people suffering from breathing problems. Some were vomiting and others had constricted pupils, they said. One woman, Maryam Khatib, later died.
A number of videos passed to the BBC appear to support these claims, but it is impossible to independently verify them. Test are being carried out in France, the UK and Turkey on samples from the site of the attack.
Mrs. Khatib’s son Mohammed had rushed to the scene to help his mother and was also injured in the attack.
“It was a horrible, suffocating smell. You couldn’t breathe at all. You’d feel like you were dead. You couldn’t even see. I couldn’t see anything for three or four days,” Mr. Khatib told the BBC.
A doctor who treated Mrs. Khatib said her symptoms corresponded to organophosphate poisoning and that samples had been sent for testing.
One device was said to have landed on the outskirts of Saraqeb, with eyewitnesses describing a box-like container, with a hollow concrete casing inside.
In another video, a rebel fighter holds a canister said to be hidden inside the devices. Witnesses claim there were two in each container.
Another video shows parts of a canister on the ground, surrounded by white powder.
The BBC has been told that samples from the scene and from the alleged victims have been sent to Britain, France, Turkey and America for testing.
Hamish de Bretton-Gordon, a former commanding officer at the UK’s Joint Chemical Biological Radiological Nuclear Regiment, said the testimony and evidence from Saraqeb was “strong, albeit incomplete”.
In Saraqeb and in three similar events in Syria in recent weeks, “people have got ill and died and their symptoms are what we would expect to see from a nerve type of agent, be it sarin or be it organophosphate,” Mr de Bretton-Gordon said.
On the available evidence, recent attacks in Al-Otaybeh to the east of Damascus, in Adra near the town of Douma, and in the Sheikh Maqsoud district of Aleppo appear “virtually identical” to what happened in Saraqeb, according to Mr. de Bretton-Gordon.
Mr. de Bretton-Gordon has not visited the site or tested any of the alleged evidence but was given full access to the material gathered by the BBC.
Both the US and UK have spoken of growing evidence that the Syrian government has used chemical weapons.
Rebel fighters have also been accused of using them. They also have denied this.
In March, Syria’s government and opposition called for an inquiry into an alleged chemical weapon attack in Khan al-Assal in the north of Syria which killed at least 27 people, with both sides blaming each other.
A 15-strong UN team headed by a Swedish scientist, Ake Sellstrom, has been assembled to investigate the claims.
However, the Syrian government has refused the team access. Syrian officials have been quoted as saying they want the team to look into the incident in Khan al-Assal, but the team has requested unconditional access with the right to inquire into all credible allegations.
The UN says estimates that the two-year-old conflict has left at least 80,000 people dead.