Hise was born July 4, 1802 in Allegheny County, Pennsylvania before moving with his parents, Frederick and Nancy (Eckstein) Hise, to Russellville, Kentucky when young. He completed preparatory studies and then attended Transylvania University, Lexington, Kentucky. He studied law and was admitted to the bar and commenced practice.
Hise was a member of the Kentucky House of Representatives in 1829. He was an unsuccessful Democratic candidate for Lieutenant Governor in 1836. He served as the Chargé d'Affaires to Guatemala, January 31, 1849 – June 23, 1849. In addition, he was the chief justice of the Court of Appeals of Kentucky.
Hise was elected as a Democrat to the Thirty-ninth Congress to fill the vacancy caused by the death of Henry Grider, and he was reelected to the Fortieth Congress. In all he served from December 3, 1866, until his death by suicide on May 8, 1867 in Russellville, Kentucky. He left behind a suicide note in which he rued "the impending disaster and ruin [of the country] in which despotic and unconstitutional rule has involved her." He was buried in Maple Grove Cemetery.
- United States Congress. "Elijah Hise (id: H000644)". Biographical Directory of the United States Congress.
- "Guatemala" (List of Ambassadors to Guatemala). United States Department of State. 2005. Retrieved August 30, 2007.
- Daily Arkansas Gazette, May 15, 1867
- Allen, William B. (1872). A History of Kentucky: Embracing Gleanings, Reminiscences, Antiquities, Natural Curiosities, Statistics, and Biographical Sketches of Pioneers, Soldiers, Jurists, Lawyers, Statesmen, Divines, Mechanics, Farmers, Merchants, and Other Leading Men, of All Occupations and Pursuits. Bradley & Gilbert. pp. 275–276. Retrieved November 10, 2008.
- Rennick, Robert M. (1987). Kentucky Place Names. University Press of Kentucky. p. 142. ISBN 0813126312. Retrieved April 28, 2013.