At the link below, you will find an official report of the 8th MSM Cavalry's engagement with forces of a Captain B. Chambers, in which Chambers was killed. He was on recruiting duty, authorized by a Col. Edward B. Hull (who later married Chapman's sister Lizzie). Hull had been Lt. Col. of the 2nd Mo Infantry, CSA, but was unaffiliated at the time. Could it be that Chambers was also not affiliated then with any particular unit, being on recruiting duty? In any case, no unit is mentioned.
Bruce Nichols, p 79 in volume III of his Guerrilla Warfare in Civil War Missouri, also mentions this engagement, which is where I saw the OR citation.
St. Joseph, MO
PS, on Fold 3 there is also a letter from a Union provost marshal asking, on behalf of Chambers' brother, "a loyal man", more particulars on the death believed to have been March 31, 1864 in Oregon Co, MO--according to this letter. You can find this letter by searching all Confederate records for Chapman, B.