Chris depends on himself in many ways. First, after graduating from college, he donates his remaining trust fund money so that he cannot rely on money he has not earned for himself to help him survive. At another point, he even burns money in his possession - he sees money (and greed for money) as a source of many problems in the world and does not want to fell prey to its controlling power. He wants to live simply, with as few possessions as possible - renouncing many of the values and priorities of the modern world, much as Thoreau has done.
Second, he does not want any personal connections to tie him down. He breaks off contact with his sister, whom he loves, because he does not want his family to know where he is. He keeps moving around so that he won't develop too deep of ties to the people he meets - although he does develop an affection for both Jan Burres and Wayne Westerberg to the point where he writes letters to them throughout his journey. He doesn't agree to let Ronald Franz adopt him and is evasive in giving him a response about when he might return.
Third, he travels alone - first, in his old Datsun until it breaks down; then, as a hitchhiker through various states. He also travels on his own by canoe into Mexico, on a journey that almost costs him his life.
Fourth, he often turns down help from those who offer it - in some cases rides, in other cases food - wanting to do everything on his own. Wayne offers to buy him a ticket to Alaska so he can stay and work the harvest longer, but Chris wants to hitchhike. When he gets a final ride in Alaska to Denali National Park, driver Jim Gallien, who is concerned that Chris is very unprepared, offers to take him back to town to buy some decent gear, but Chris refuses. Jim finally convinces him to at least take an old pair of rubber boots and the sack lunch he has in his truck.
Finally, Chris doesn't even take a proper map into Denali - he wants, like pioneer, to find his own way. A proper map would have helped him considerably when he finds himself stuck: it would have shown him where he could cross the river, and it would have shown him some cabins where he might have been able to find some supplies. Instead, unable to cross the river, he dies starving and alone.
Did you mean "depend" in your question? If so, he kept to himself in the forest by hunting caribou and eating wild plants. Before he'd separated from society, he'd donated all his money to charity and waltz into the forest with only a few supplies and a bag of rice. Unfortunately, he'd burned more carbs than the intake, slowly killing himself. He'd gone unprepared into the woods, believing it would be easy to adapt to that lifestyle. Sorry if my answer wasn't what you were looking for. Your question sort of threw me off.