There are some different laws surrounding Chicago and Cook County's handgun magazines.
Here is Cook County's law regulating handguns
Here is Chicago's law regulating handguns.
"High capacity magazine” means a magazine, belt, drum, feed strip, or similar device, including any such device joined or coupled with another in any manner, that has an overall capacity of more than 15 rounds of ammunition. A “high capacity magazine” does not include an attached tubular device to accept, and capable of operating only with, .22 caliber rimfire ammunition
It is unlawful for any person to carry, possess, sell, offer or display for sale, or otherwise transfer any high capacity magazine or tubular magazine extension for a shotgun.
It shall be unlawful for any person to manufacture, sell, offer or display for sale, give, lend, transfer ownership of, acquire, carry or possess any assault weapon or large capacity magazine in Cook County
"Large-capacity magazine" means any ammunition feeding device with the capacity to accept more than ten rounds, but shall not be construed to include the following:
A feeding device that has been permanently altered so that it cannot accommodate more than ten rounds.
Does this apply to anyone with a valid CCL?
The Illinois state law:
(430 ILCS 66/90) Sec. 90. Preemption. The regulation, licensing, possession, registration, and transportation of handguns and ammunition for handguns by licensees are exclusive powers and functions of the State. Any ordinance or regulation, or portion thereof, enacted on or before the effective date of this Act that purports to impose regulations or restrictions on licensees or handguns and ammunition for handguns in a manner inconsistent with this Act shall be invalid in its application to licensees under this Act on the effective date of this Act. This Section is a denial and limitation of home rule powers and functions under subsection (h) of Section 6 of Article VII of the Illinois Constitution. (Source: P.A. 98-63, eff. 7-9-13.)
Would this Preemption make Chicago and Cook County's restrictions on handgun magazines invalid?