Chicago (or most US cities) are bad example for many reasons, but the primary one is that most of the guns used in crimes do not actually come from Chicago, but a different county or state all together. There's a reasonable argument that it's not that Chicago has ineffective laws, but rather that the areas around it have lax laws and Chicago is worse off for it. Think of a place like Hawaii: strict laws and geographical isolation combine to have the lowest rates of gun violence in the country (not for long if
@alanb has anything to say about it). Even California, with its troubled urban areas has relatively low gun violence per capita. This is mostly due to tough laws statewide and that the city centers are isolated from other states with lax laws.
Re: "guns aren't the problem, people are" - no shit. The problem is the bad guys have access to guns. The goal should be 2 pronged: do something about the bad guys AND do something to prevent them from getting guns. This isn't rocket science. Ask yourself this: would London today as a whole be better off with more handguns in circulation? What about in 5-10 years after the refugees have initially moved in?