I'm not 100% sure what the Nike+ kit is, I thought it was a custom protocol, in the same frequency as Bluetooth, ANT or XBee, but I think not the same protocol. Wikipedia says that it is ANT, but looking at it, there isn't any evidence for that, and the fact no one has got it talking to other devices suggests it isn't ANT (and the fact the Nike+ units don't appear to talk nicely with a standard ANT receiver).
Oh actually a little digging, and it appears that it is a non-standard protocol, so no luck there.
What you need is an external receiver – there is one I know of:
http://en.pedalbrain.com/pricing
These people have an external ANT transmitter that talks to things like powertap hubs and suunto heart rate monitor straps and all that gubbins.
Not cheap mind, $200 for the bit to connect to the iPhone, plus a subscription that you have to pay to use it.
Or a bluetooth heart rate strap. There are a few of these, but they are all either very expensive medical things, custom built, or the Nokia thing, which is not possible to buy separately, and probably locks itself to only talk to Nokia phones.
Joe