Brigadier General James Chestnut was the husband of Mary Chestnut, whose diary was extensively quoted in Ken Burns' Civil War documentary.
In my quest for my ancestors, I have seen how inconsistent name spelling was before compulsory education last century.
I too would assume that officers would be literate and familiar with the spelling especially those on the staff of a General and doing his reports but you never know. Maybe the error was with the person doing the inscription. All through the 1800's and as recently as the 1880 census, I have seen the various names in our ancestry written numerous ways by the census takers. I guess the Anglo-American census takers had trouble with our Irish brogues and Hessian accents. Ancestry.com search uses Soundex and other algorithms to find all the different spellings that might fit someone's name. It is amazing how many official documents (deeds, wills, etc.) have them misspelled. It seems that the Chesnut/Chestnut family has suffered similarly:
http://louisianalineagelegacies.blogspot.com/2007/09/family-of-james-chestnut-jr-marys.html
http://donchesnut.com/genealogy/pages/chessurn.htm
It appears my spellchecker has initiated a kerfuffle. I shall send it to bed without dinner. I hope I don't need that extra "t" that it carelessly threw away.