A version for acoustic guitar without all the Guthrie-enhanced shoegazer effects
As nobody knows exactly what Liz is singing, I took generic lyrics from a Cocteau Twins Wiki

Standard chord transitions:

Intro Verse D-G-D-G
Chorus D-(C-Cadd9)-D-(C-Cadd9)
Interlude and End Em-A-C-G(-A for end)

Riffs for:

Intro & Verse
   D               G
e|--9---------------2----------|
B|----10--------------3--------|
G|-------11-------------4------| Riff continues
D|----------12------------5----| through verses
A|-----------------------------|
E|-----------------------------|

Chorus
e|--5---------5--------5----|
B|--------5-7-------5-7-----|
G|------7---------7---------|
D|--------------------------| Repeats
A|--------------------------|
E|--------------------------|

Chords->


D G X 2

            D
Who'll ever win?
                        G
Gee, you're just so ephemeral
            D
Go back for new
                    G
For new in vain, it failed

D                           C Cadd9
Singing on the famous street
          G
I want to love (a love...) me
D                              C Cadd9
Am I just in heaven or Las Vegas
                  G
It's so much more brighter than the sun is to me


            D
He's a hustler
                                G
It's a role, he'll never make a suit
           D
Hang on to this
                                G
So stay and spin and fail and fail

            D
Who'll ever win?
                        G
Gee, you're just so ephemeral
            D
Go back for new
                    G
For new in vain, it failed

D                           C Cadd9
Singing on the famous street
          G
I want to love (a love...) me
D                              C Cadd9
Am I just in heaven or Las Vegas
                  G
It's so much more brighter than the sun is to me

D                              C Cadd9
The chill must itch in my soul (Heaven or Las Vegas)
G
That's like any old playing card
               D                        C Cadd9
It must be why I'm thinking of Las Vegas (Heaven or Las Vegas)
                                        G
It's why it's more brighter than the sun is to me

Em                 A
Furthermore, let's blast it off
    C Cadd9         G
I'm dizzy so I go, another bit it off
    Em              A
Come fantasy, for a carnival
    C Cadd9          G
I'm empty before our wedding

Oooooh
Em A C G X 2

D                           C Cadd9
Singing on the famous street
          G
I want to love (a love...) me
D                              C Cadd9
Am I just in heaven or Las Vegas
                  G
It's so much more brighter than the sun is to me

D                              C Cadd9
The chill must itch in my soul (Heaven or Las Vegas)
G
That's like any old playing card
               D                        C Cadd9
It must be why I'm thinking of Las Vegas (Heaven or Las Vegas)
                                        G
It's why it's more brighter than the sun is to me



Em                 A
Maybe there, while you was rail
        C Cadd9                 G
I'll go in and seize your heart and be personal
Em           A
I suspect I'm singing to you a tune
    C Cadd9                     G
And still you find the beat and sing it to you soon

Em A C G
Em A C G A End