The Grateful Dead first played this when they were the Warlocks in 1965. They played it a few times through their career, most frequently in 1992 and 1993.
This is the version from 1 November 1985, on Dick's Picks 21.
Let me tell you about my baby
Yu know she come around
Just about five foot four
From her head on up to the ground
When she come around here
Just about midnight
Oh she only comes to make me feel so good
She only make me feel alright
And her name is G.L.O.R.
Now wait a minute
G.L.O.R.
Wait a minute, wait a minute, wait a minute, wait a minute
Said her name is G.L.O.R.I-I-I-I-I-I.A., G-L-O-R-I-A
(Gloria) G-L-O-R-I-A
(Gloria) I wanna to shout it every night now
(Gloria) I wanna to shout it every day
(Gloria) Hey, hey, hey, hey, hey
Tell you about my baby
Walking down the street now
Me and my little baby
She's walking along with two feet now
She's walking round here
Just about midnight
She only come to make me feel good
Oh, she make me feel all right
She come walking down my street
Then she come up to my house
Knock upon my door
And then she come into my room
Hey, then she makes me feel all right, all right
Then after that I can never figure out where my baby went
She might have gone off on a space shuttle
Or gone and run for President
Don't matter much to me now
'Cause she makes me happy as I can be now
And child
And her name is G.L.O.R.
Wait a minute
Sometimes it's hard to get it all together
When you want to try to spell now
What you gonna me be now, somehow I can tell now
And her name is G.L.O.R.I-I-I-I-I-I.A. G-L-O-R-I-A
(Gloria) G-L-O-R-I-A
(Gloria) I wanna to shout it every night now
(Gloria) I wanna to shout it every day
And her name is G.L.O.R.I-I-I-I-I-I.A. G-L-O-R-I-A
(Gloria) G-L-O-R-I-A
(Gloria) I wanna to shout it every night
(Gloria) I wanna to shout it every day
(Gloria) G-L-O-R-I-A
(Gloria) G-L-O-R-I-A
(Gloria) G-L-O-R-I-A
(Gloria) G-L-O-R-I-A