The iPhone 4, as I understand it. But when iOS 7 comes out, it'll be a good opportunity to upgrade. Even if the iPhone 4 will run it, it doesn't mean it will run it well. Might as well grab some new hardware and enjoy iOS 7 the way it was meant to be enjoyed.
iPhone 4 is the oldest officially listed as compatible. Not all features may work on the older devices though (it’s a little weird for me to think of an iPhone 4 as an “older device”). Siri, for example, will only work with iPhone 4S or later.