The legal grounds for any military action against Syria are actually very straightforward. Without UN authorisation, there are none.
Assuming that the use of chemical weapons can be legally attributed to Syria, its government is in breach of the 1925 Geneva Protocol, which prohibits the use of such weapons.
However, the Protocol in no way authorises other states to respond with military force.
The UN Charter is clear that any use of force against another state is prohibited, unless this is an action of self-defence or is authorised by the Security Council.
– Dr James Green, International Law Expert
With regard to Syria, self-defence is definitely out, as there has been no attack against another state, or even the imminent possibility of such an attack.