Buy it from Best Buy. Best Buy sells the iPhones subject to the US Reseller Flex Policy so they all have the Qualcomm chip. Once you pay it off in full, AT&T will unlock it for you and it will work on Verizon fine.
If you pre-order through Best Buy, ship to home or ship to store, they do not come with the SIM cards pre-installed. And if you use a Verizon postpaid SIM card for the initial activation, the phone will be unlocked from the get go. the Verizon SIM card does not have to be active, you can use an inactive Verizon SIM card for the initial activation and activate over WiFi or using iTunes.
Then put your AT&T SIM card in the phone to use it on your AT&T line.
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No but you can pre-order through Best Buy and you will get a phone with the Qualcomm chip even though they call it an "AT&T" phone since BB sells the iPhones subject to the USRFP. And if you use a Verizon postpaid SIM card for the initial activation, the phone will be unlocked from the get go.
Best Buy also charges a $100 up-charge on iPhone models sold at full retail price.