Is there an FM radio app for the iPhone? I am planning to buy an iPhone, but the one thing missing is FM radio. 

Is there a way to listen to FM radio on the iPhone?
There's no good public answer for this question. There is an FM radio in the iPod Nano, but leaving it out of the iPhone is clearly a design decision. There may have been issues with chip suppliers, but I suspect that had Apple wanted to have an FM radio in the device, those issues would have been dealt with.

It's somewhat more likely that Apple sees FM radio versus material it sells or rents via the iTunes Store as a zero-sum game. Consuming more of the former makes it somewhat less likely that the latter will be purchased.

Given the famous Apple disdain for focus groups and market research, it's probably most likely that someone in an iPhone design meeting said "Hey, who listens to FM radio?" and got no reply, so that feature was cut