What can you infer about Chris's relationship with Wayne in the beginning of Chapter 1?

Purely based upon the letter, we can infer that Chris and Wayne are good friends. He's taken the time to write the letter, to let Wayne know he arrived in Alaska safely, and to share the news that he is about to begin his journey. We also get a sense that Chris hasn't been completely honest with Wayne. He respects him and calls him a "great man", but he doesn't sign his real name. Based upon this first chapter, we don't know if Westerberg really knew who Chris (Alex) was. It isn't until Chapter Three that Wayne did learn his real identity.

At one point Westerberg discovered from a tax form that McCandless’s real name was Chris, not Alex. “He never explained why he’d changed his name,” says Westerberg. “From things he said, you could tell something wasn’t right between him and his family, but I don’t like to pry into other people’s business, so I never asked about it.”

Chapter Three also tells us the following;

Driving west out of Atlanta, he intended to invent an utterly new life for himself, one in which he would be free to wallow in unfiltered experience. To symbolize the complete severance from his previous life, he even adopted a new name. No longer would he answer to Chris McCandless; he was now Alexander Super-tramp, master of his own destiny.