I think the saying that "when guns are outlawed, only criminals will own guns" has finally moved from a truism to an axiom. Chicago has some of the strictest gun control laws in the nation and so, of course, it also has one of the highest gun crime rates. But the violence has clearly moved beyond just Chicago's restrictions to federal restrictions on gun ownership.
When it was enacted in 1934, the creators of the National Firearms Act were frightened that the law would be struck down as unconstitutional for violating the Second Amendment because it banned the unorganized militia (i.e., the citizens) from owning military weapons, including fully automatic weapons. To try and avoid such an outcome, the NFA creators decided against an outright ban and settled on a tax (ostensibly under the Congress' taxing authority) to make the weapons so prohibitively expensive that no one but the rich would be able to afford them. Even so, the creators were correct in their fears: in United States v. Miller, 307 U.S. 174 (1939), the Court came close to striking down a provision of the NFA taxing the purchase or possession of short-barreled shotguns and only siding with the U.S. attorney general because the U.S. argued that short-barreled shotguns had no military purpose and, therefore, were not protected by the Second Amendment. Presumably, if someone had challenged the restrictions on owning an automatic, military style weapon, the Court would have struck down that portion of the NFA because such a weapon had a military purpose.
But the NRA had supported the NFA and no else apparently pursued such a case, so in the face of numerous bans on classes of firearms, there still remains the anomaly that a person can purchase a fully automatic weapon provided that they can pass the background checks and pay the tax on such weapons. But just as inflation reduced the amount of the tax to something that would make such weapons affordable to the middle-class, the anti-gunners decided to once again make them too expensive to afford, but this time they attacked the supply side of the equation by making the manufacture of automatic weapons illegal. So, just as demand was beginning to increase, the supply was cut, and prices quickly climbed to the point that the rich are still the only ones that can afford the weapons.
But how has that worked out? Not very well. We've seen an increasing number of accounts of automatic weapons fire between criminals. The most recent I came across was an article from the Daily Mail reporting that "'Chicago is a war zone': Terrifying video shows machine gun fire erupting on the streets in bloody Thanksgiving weekend of gun violence as three are killed in [sic] and another 40 are shot." The story includes the video and describes it as showing "a man, who does not appear to have a gun, running through the streets of Chicago as machine gun fire erupts nearby." It doesn't show the weapons, but you can definitely hear a couple bursts of automatic weapons fire. So, yes: if you make a class of weapons illegal, whether de jure or de facto, only the criminals will have them.