A front page article in today's Times tries to answer that (my emphasis):
More than a quarter of the firearms seized on the streets here by the Chicago Police Department over the past five years were bought just outside city limits in Cook County suburbs, according to an analysis by the University of Chicago Crime Lab. Others came from stores around Illinois and from other states, like Indiana, less than an hour’s drive away. Since 2008, more than 1,300 of the confiscated guns, the analysis showed, were bought from just one store, Chuck’s Gun Shop in Riverdale, Ill., within a few miles of Chicago’s city limits.
At the store, a clerk said the business followed all pertinent federal, state and local laws, then declined to be interviewed further. Among seized guns that had moved from purchase to the streets of Chicago in a year’s time or less, nearly 20 percent came from Chuck’s, the analysis found. Other guns arrived here that rapidly from gun shops in other parts of this state, Indiana, Wisconsin, Kentucky, Mississippi, Georgia, Iowa and more.
“Our gun strategy is only as strong as it is comprehensive, and it is constantly being undermined by events and occurrences happening outside the city — gun shows in surrounding counties, weak gun laws in neighboring states like Indiana and the inability to track purchasing,” Mayor Rahm Emanuel said. “This must change.”
“Chicago is not an island,” said David Spielfogel, senior adviser to Mr. Emanuel. “We’re only as strong as the weakest gun law in surrounding states.”