Nine men from the regiment were recommended for the Medal of Honor, one from each company except Company E.

"Fighting with remarkable courage at the Battle of Chickamauga, in September 1863, nine men of the old 31st Arkansas were awarded the Confederate equivalent of the Medal of Honor."

Private Jonathan Pool, was awarded the Confederate equivalent of the Medal of Honor for his heroism at the Battle of Chickamauga.
Sergeant J. Greene Read, was posthumously awarded the Confederate equivalent of the Medal of Honor
Private James N. Garvin,
Private William H. Huie
Sergeant John N. Cannon
Sergeant James W. Carter
Private Francis M. Arnold,
Sergeant George W. Williams,
Private James E. Coker

Checking the records of two men, I found

Privates Jonathan Pool, Co. A and James E. Coker, Co. K, are recorded as having been placed on an Honor Roll August 10, 1864, re General Order Number 64/2

The Confederate States of America created their own version of the Medal of Honor in October 1862, by authorizing President Davis to bestow medals to officers for courage and good conduct on the field of battle, and a badge of distinction to privates and non-commissioned officers after each victorious battle. Unlike the U.S. criteria for awarding the “Medal of Honor,” the Confederate criteria rested with the soldiers themselves. Company non-commissioned officers and privates selected by majority vote the one soldier in their Company that best deserved the “Badge of Distinction”. Due to the shortage of metal, the Congress of the Confederacy in October 1863, created the “Roll of Honor” to list those officers, non-commissioned officers, and privates deserving of medals and the “Badge of Distinction” with the intent of awarding medals at a later time.
http://mohm.org/recipient_pages/moh_recipient_history.html

See also: http://www.fold3.com/page/915_confederate_medal_of_honor/