Will Apple replace my iPhone battery?

My iPhone 4 recently shut down completely and will not turn on at all. I took it to an Apple store today and it turns out that the phone is fine, but the battery is dead. The Genius said the battery could easily be replaced.. for $79. My question is, if I buy the battery cheaper elsewhere, will Apple still replace it for me? Thanks in advance!

Go to this website:

iPhone Repair - iFixit

Choose your iPhone model...and replace the battery yourself.

- Nick

What Nick is saying is "no, they won't."

And the battery along with the screw drivers you need here. Along with their how to video, you can become your own $50+/hour tech support.

Considering how soon some folks need to replace their batteries, am amazed with the two 3GS phones I'm still using.
Mine still goes for about 1.5-2 days depending on what I'm doing with it and the wife's lasts her 3-4 days.
Both, still the same as when new 4+ years ago now.

My original iPhone's battery still works, not as well as it did in 2007 but several hours still.

My iPhone 4 battery is as good as ever after three years.

To be perfectly fair, many people use/cycle their iPhone batteries harder than I do.