Isn't Chicago only running a 5 MHz LTE carrier (5 up/5 down - 10 total)? Most AT&T markets and all Verizon markets are running 10 Mhz (up/down - 20 total) for LTE.
Compare that to UMTS (HSPA+) - which has a fixed carrier size of 5MHz (DC-HSPA+ allows it to be channel bonded to virtually "act like" it's 10). Most markets are running many channels of UMTS.
Even here in rural Montana, AT&T has two UMTS carriers in the majority of the populated area (oddly, not downtown Kalispell - though it's still much better than when they first launched and all of Kalispell was one carrier - because the second carrier still leaks from surrounding sites outside. It's odd going from one bar outside, walking in a building, and suddenly getting five bars LOL. Because they steer on to the PCS carrier from distant sites most of the time since it's less loaded. Doesn't cause any problems at all, just weird because of the very minimal "bars" outside downtown, and full bars inside buildings). In larger cities around the country, more UMTS carrier channels are the standard. New York City I believe has five UMTS carrier channels. I've heard of as many as six being ran in some places where AT&T has lots of spectrum and a hard time building towers (the more people a site reaches, the more capacity it needs. Building more sites and shrinking the coverage of each one is a good option - but the darn NIMBY's ruin that one too often)
Granted, LTE *is* more efficient than UMTS. UMTS, with HSPA+ as deployed by AT&T has a theoretical forward link data rate of 21mbps. This can be increased to 42mbps with MIMO (allowing DC-HSPA+ with MIMO to reach 84mbps). 5MHz of LTE has a theoretical forward link data rate of, I believe (LTE is more complex and has many coding schemes), somewhat under 50 mbps (perhaps 43? Though I don't recall exactly).
LTE isn't so amazing as people think

90% of LTE's benefit, TODAY, could be achieved by upgrading UMTS networks to support MIMO. LTE-Advanced is where it's at.
The benefits seen by first-generation LTE come from a lack of users on the new network and the fact the network isn't being used by voice and SMS (SMS in tiny, but has a somewhat bigger impact than the small sizes would suggest due to it using control messages. SMS was never designed for a world where it would be a service being used by each subscriber thousands of times each month).
Long story short, AT&T's LTE in Chicago supports about the same amount of data traffic as two UMTS channels today would, or one MIMO UMTS channel. You're not going to see huge speed improvements from UMTS, and once more people are on it it could even easily be substantially slower. That's why AT&T needs the Qualcomm spectrum and LTE-Advanced (or at least the asymmetrical forward link channel bonding). It's why AT&T wanted T-Mobile... and it's also why AT&T is considering refarming 850MHz (the cellular band) for LTE....