The team made the announcement Tuesday. Chavez's deal is not guaranteed.
He went 2-4 with a career-low 3.92 ERA and one save in 35 appearances over two 2013 stints with the two-time defending AL West champions. He made $500,000.
Oakland's remaining players eligible for arbitration include catcher John Jaso, new closer Jim Johnson, right fielder Josh Reddick, first baseman Brandon Moss and shortstop Jed Lowrie.
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