The Syrian government has various treaties against the possession and use of chemical weapons. Say (as seems likely) that recent chemical chemical attacks in Syria were undertaken by the government. Would any of these treaties give the United States permission to punitive miitary actions?
Article 42 of the U.N chapter allows for an attack only when international peace or stability is threatened, and article 51 allows for military attacks in self defense. Neither of them seem to be applicable in this case.
The Security Council may decide what measures not involving the use of armed force are to be employed to give effect to its decisions, and it may call upon the Members of the United Nations to apply such measures. These may include complete or partial interruption of economic relations and of rail, sea, air, postal, telegraphic, radio, and other means of communication, and the severance of diplomatic relations.
Should the Security Council consider that measures provided for in Article 41 would be inadequate or have proved to be inadequate, it may take such action by air, sea, or land forces as may be necessary to maintain or restore international peace and security. Such action may include demonstrations, blockade, and other operations by air, sea, or land forces of Members of the United Nations.
Nothing in the present Charter shall impair the inherent right of individual or collective self-defence if an armed attack occurs against a Member of the United Nations, until the Security Council has taken measures necessary to maintain international peace and security. Measures taken by Members in the exercise of this right of self-defence shall be immediately reported to the Security Council and shall not in any way affect the authority and responsibility of the Security Council under the present Charter to take at any time such action as it deems necessary in order to maintain or restore international peace and security.
It is also potentially a violation of the U.S constitution. In Trump's own words:
The President must get Congressional approval before attacking Syria-big mistake if he does not!