See no obvious signs that it isn't, but I'm not an expert. If it's a fake it's a really good fake. I'd say with 98% certainty it's real but wait for people who know more about such things than I to chime in. I don't see anything wrong with it, and it has all the things a genuine note of this type should have. And people don't bother to fake this kind of thing often; too complicated, better percentage in faking currently circulating notes and passing them off than trying to fake collectable notes to sell to unsuspecting collectors. And while this note is in decent condition for its age, if one were to try to fake it for the sake of selling to collectors they would either have left it in mint condition or attempted to artificially age it more. Probably would have centered it better too (the note is slightly off center, but not to the degree it would be considered an error).
I like large sized nats that are dated in the 1920s myself. I did own one for awhile that was dated 1927, so one of the last charters before they switched over to the small sized notes the following year. This particular bank was chartered in 1881 and there are 21 large notes and 18 small notes reported for it in the census. The value is in the range of $350 per the Kelly reference. Per the Kelly census this note is currently NOT REPORTED - so it may be a discovery piece.