If you are referring to the book Lord of the Flies, then he became chief on page 181. Right after Piggy was killed.
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It seems that Roger has become the unofficial second in command to Jack and also chief torturer.
Chief Jack House died in 1971.
Piggy is fully aware that Ralph is the only thing that is preventing Jack from becoming chief. Piggy knows that if Jack does become chief all hope of rescue will disappear because Jack will only bother about hunting and the signal fire wil be forgotten. Piggy is also fearful for his own safety.
Ralph is elected as the chief but Jack assumes the role of chief of the hunters.
Jack Godfrey's real first name is John