A couple of months ago I was in Palo Alto, CA visiting some friends. We ran across a place on Emerson St. (just off University Ave) called "Patxi's Pizza" (pronounced pah-cheese).
It said Chicago style pizza, so I thought I'd give it a go. I was absolutely amazed at how close it was to Giordano's. I am pretty much a pizza snob...Giordano's is the deep dish/stuffed pizza by which I measure all others. The only thing I had ever had before that was close to Giordano's was Zachary's in Berkeley, CA...but is definitely different than Giordano's.
Patxi's on the other hand has nailed it.
Their Palo Alto store has done so well, they opened a second location in San Francsico off of Hayes. I highly recommend giving them a try! It's as close as you are going to get being this far away from Chicagoland!http://www.patxispizza.com/