The Syrian government appears to have used chemical weapons in its civil war. The BBC has seen video and eyewitness testimony that appears to corroborate allegations of chemical weapons' use in the Syrian town of Saraqeb. The United States has seen sufficient evidence of the use of chemical weapons to be convinced as well, though that may be less persuasive to some. As the Guardian reports, Medecins Sans Frontieres also corroborates the allegations.
(Although there have been suggestions that the rebel groups would be motivated to employ chemical weapons, there is less independent evidence that any of the rebel groups opposing Assad possess such weapons. Moreover, the use of chemical weapons by one or more rebel groups doesn't rule out use by Assad and vice versa. Welcome to the civil war.)
The use of chemical weapons is a clear violation of one of the few widely respected tenets of international law. International law is only as strong as the willingness of the strongest supporters of international law to enforce it. Currently, those supporters are the United States and to a lesser extent the UK and France. So, either we act against Syria or the international law against the use of chemical weapons is weakened.
Upholding international law and saving innocent civilians are not the only interests that we have in Syria. Most of our other interests in Syria are facilitated by intervening against the Assad regime (disrupting the flow of arms to Hezbollah; opposing state supporters of terrorism; reducing Iranian and Russian influence).
Further, the United States has a strong interest in maintaining its credibility and President Obama previously stated that the use of chemical weapons would be a redline for the United States Obtaining a reputation for not following through on threats and commitments can be very expensive for a country. That is a powerful, albeit self-inflicted, reason to act.
However, we do have some interests that are not likely to be advanced by intervening in Syria and we should think seriously about those before we intervene:
Most importantly, we have a very strong interest in preventing the proliferation of chemical weapons especially to groups affiliated with al-Qaeda. A number of rebel groups are affiliated with al-Qaeda and if the Assad regime were to fall, those groups would have a significant chance of obtaining chemical weapons. Further, an attack focused on chemical weapons depots or chemical weapons associated infrastructure, even if it doesn't topple Assad, would also increase the likelihood of an al-Qaeda affiliated group obtaining access to chemical weapons. That would argue that securing chemical weapons would need to be a significant part of any intervention which would imply at least some use of ground troops. It should be noted that we are unlikely to use ground troops to intervene, for obvious reasons. Evidence of use by rebels of chemical weapons suggest this concern may be moot; but, even if the rebels have some chemical weapons we continue to have an interest in minimizing there proliferation.
If we smash Assad using airpower alone, Syria will likely fracture and descend further into civil war. Whether the eventual outcome of this is better off for the United States than the current situation is unclear and whether this is more destabilizing to surrounding countries (which would not be in American interests) is also unclear.
It is also relevant to note that neither the countervailing interests nor the interest in maintaining American credibility were present in the Libyan situation.
We also need to consider that Assad probably has the support of about 15% of the population plus external supplies from Iran and Russia. This situation is very different from the situation in Libya or Afghanistan. It also differs from the situation in Iraq.
While I've noted an awfully large number of disingenuous arguments against intervention on this site, and am tentatively in favor of intervening, we also need to think about the limits of our intervention and its goals. So far, these have not been articulated. While American intervention may be warranted here, we need to have a clear understanding of the goals and limits of that intervention before we embark on it.