Ralph is elected chief during the very first meeting, which happens very early in the book.
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Ralph becomes the chief in the first chapter after there is a vote between Ralph and Jack.
Ralph is elected as the chief but Jack assumes the role of chief of the hunters.
chief
During the first meeting, which was held in chapter 1: The Sound of the Shell, Ralph was elected as the chief. Later in the book Jack formed his own tribe and appointed himself as chief.
Ralph
Jack wants power and Ralph, as the elected chief, has it. People tend to judge other people by their own motives. So, even when Jack manages to seize power and become chief of his tribe of savages he can't believe that Ralph would be prepared to accept this. He fears that Ralph will act as he would act himself and will eventually regain control. For this reason Jack wants to destroy him. As far as Jack is concerned while Ralph remains alive he will always be a threat to his authority.