They must have missed the "shall not be infringed" part. 

Via Liberty Park Press: 

A pair of Illinois lawmakers have introduced national licensing and registration legislation that, according to rights activists, clearly illustrates how anti-gunners view the Second Amendment right to keep and bear arms as a government-regulated privilege...

The proposed act “would prohibit unlicensed gun-ownership and transferring or receiving firearms without a valid firearms license, as well as direct the Attorney General to establish and maintain a federal record of sale system,” the press release details.

According to the Washington Examiner, if this bill becomes law, it will “require a valid firearms license for transferring and receiving guns…require universal background checks for all sales and transfers of guns, and would make it easier for state and federal officials to trace guns.”

Read more here.