Gilhams was elected as a Republican to the Fifty-ninth Congress to fill the vacancy caused by the resignation of Newton W. Gilbert.
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He was an unsuccessful candidate for reelection in 1908 to the Sixty-first Congress.
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He was reelected to the Sixtieth Congress and served from November 6, 1906, to March 3, 1909.
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Born in Brighton, Indiana, Gilhams attended the common local schools and Indiana State University at Terre Haute, Indiana and became a school teacher.
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