The answer to this question can be found in Chapter Seven, which details Chris's time working in South Dakota with Wayne Westerberg on his farm. Although Chris did not spend much time in this location, he chose this to be his permanent address in terms of where he wanted his mail to be sent. Note what he wrote to Wayne in the last postcard that he sent:
Please return all mail I receive to the sender. It might be a very long time before I return South.
This shows that Chris McCandless chose this location to be his permanent address and had all mail sent to this location. Let us remember that Chris had turned his back on all of civilisation in his desire to go "into the wild," and leaving his mail and correspondence like this was just another symbol of his rejection of civilisation.