As far as I know, tf, that's the way Mr. B. wrote it. Guitarists who aren't comfortable with movable chords should feel free to transpose at will. (Or at anybody else if Will isn't interested.) Although, as with many Tin Pan Alley and jazz tunes, the individual chord names are only an approximation of moving melody, bass, and internal melodic lines in the accompaniment, so standard open position chords don't really do it justice. (Spoken by someone who understands chords a lot better than he can play them!)

Glad to help, Fergie. I hope Granny enjoys it!

Aloha,
Mark