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Brinegar joined the Union Oil Company (later called Unocal Corporation) in 1953 as an economic analyst and held several positions in economics, planning and research until 1965, when he was elected vice president for corporate planning. In October 1965, Union Oil and the Pure Oil Company merged. Brinegar was appointed president of Pure Oil and remained in that position when Pure became Union 76. He was also elected senior vice president of the firm and a member of Union Oil's board of directors and executive committee.