Lonewolf,
They did not sign the Chemical Weapons Convention, but they did sign the Geneva Protocol. Unfortunately that does prohibit the manufacture or stockpiling of CW, just its use, which some folks seem to think they have.
Syria is a member of the UN and, so, I guess they are bound by the existing resolutions. For example, UN Resolution 1540, which mostly about proliferation, but I haven't read the entire thing so there may well be bits in it about production, stockpiling and deployment.
Like you, just thinking.