William,
A quick search of some files on the internet provided the following information:
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Chilton Reed
Enlisted as a Sergeant on 01 September 1862
Enlisted in Company H, 2nd (Duke's) Cavalry Regiment Kentucky on 01 September 1862.
2nd Regiment, Kentucky Cavalry (Duke's)
2nd (Morgan's) Cavalry Regiment was organized during the summer of 1862 using Morgan's Kentucky Cavalry Squadron as its nucleus. The unit contained men from Kentucky, Texas, Mississippi, and Alabama. It served in Morgan's Brigade and was active in Tennessee, Kentucky, and Ohio. Many were captured in the conflict at Buffington Island on July 19 and the remaining part at New Lisbon on July 26, 1863. The regiment was not reorganized. Its field officers were Colonels Basil W. Duke and John H. Morgan, Lieutenant Colonels James W. Bowles and John B. Hutcheson, and Majors G.W. Morgan and T.B. Webber.
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I hope that this is of some help.