Allen was born in Rockbridge County, Virginia, and moved with his father to Kentucky in 1779. He went to school in Bardstown, Kentucky and studied law in Staunton, Virginia. He then returned to Kentucky to law practice in Shelbyville. He was elected to the Kentucky Senate in 1807, and served until his death.
Early in the War of 1812, Allen raised the 1st Regiment of Riflemen to serve under General William Henry Harrison. Allen was commissioned its colonel. He was killed in action while leading his men at the Battle of Frenchtown on the River Raisin in southeast Michigan. He is buried in Frankfort Cemetery in Frankfort, Kentucky.
Allen County, Kentucky was named for him in 1815. He is also honored by Allen County, Ohio, and Allen County, Indiana.