Very simple song, but a lovely one.  Get intimate with that ol' harp and the parlour's 
collective jaws will drop.

INTRO: CGC5 C5
       FG5  C5

Just play that over and over and over.  To wit:

C5                     G5     C5             C5 (032310)
Little Ann's in the kitchen in her modern gown
F5              G5               C5
With the rainy weather coming down
Oh the radio does play
I could sweep you off your feet
But you're two teary eyed to even know

Little Ann, Little Ann let that stormy weather go
From your front door to the heart of Chicago

Oh the lightning and the thunder
Are rolling in the sky
Coming down just like your teary eyes
Oh Annie don't you cry
If youre crying for me, when you're gone I'll find some company

Little Ann, Little Ann let that stormy weather go
From your front door to the heart of Chicago
Little Ann, Little Ann let that stormy weather go
From your troubled mind to the heart of Chicago