I believe that's what is referred to as the Peanut Guitar.
 
Sam

Sam's right.
There's a better picture here.
See also here.

In the Grateful Dead gear book, Rick Turner explains that guitar is a body he made (with a local furiture maker) with a Les Paul custom neck he salvaged.  Rick used it as his main guitar in the late 60's with Autosalvage until Jerry bought it.  
 
It has been recorded in (I think) Stepping Out with the Grateful Dead a circa '71 performance.  It aya have been Ladies and Gentlemen, The Grateful Dead also.  I don't have the book in front of me.  
 
Rick is quoted as wishing he knew where that guitar is now.

On a recent Interscope record by Sierra Swan, I use my 77 custom exclusively. However I don't know how many of the 5 tracks I did survived the major label bloodletting, and I know Linda Perry redid some of our tracks note for note. Anything produced by Bill Bottrell is me on my Alembic.  
 
DS

One of Alembics was used by a buddy of mine on a dance club album by someone named Michelle Weaks.  or something like that.  I guess she's big in Big Gay Dance Party crowd.  This was about 4 years ago.  I never heard the album.  wasn't my thing.  But apperantly the producer was floored by the sound of my bass.  
 
Hey DW, how is my old girlfriend anyway?

Your first post here, Dan??!!  I'm surprised you weren't one of the charter members given how long you've been part of Alembic Nation!
 
Paul

Has somebody mentioned Bowie guitarist Carlos Alomar yet, who has played his Alembic guitar on albums such as Scary Monsters and has toured with Bowie during the eighties using his Alembic as his main stage guitar.
 
If nobody has mentioned him, I'll mention him right now.

Alomar's 1975 Alembic guitar. A guitar heard on MANY classic Bowie albums.

Blazer,
 
Did Alomar use the Alembic on Ashes to Ashes?  That track has otherworldly guitar sounds.

I wouldn't be surprised if he did but Bowie also had deployed Adrian Belew on that track and he's probably the man behind those otherworldly guitar sounds.

And then there is John Mcvie!

Marvin Isley of the Isley Brothers played a Series II bass on the Go For Your Guns album.  The sound is distinct.

Hello, Vann. Welcome to the club!

Welcome to club Vann
 
I loved the Go For Your Guns album.  
The band I played with in high school did a cover of Climbing Up The Ladder. Cool song.

Mark King used Alembics on Staring At The Sun through to Guaranteed although for the recording he used a Musicman for about 80% of the recording.
His Alembics were his main stage basses, he hardly uses them now preferring his own designed Status basses with small body, headless neck and led's

Marvin Isley shines on the entire Go For Your Guns album.  The bass and guitar lines on 'Climbing Up The Ladder' are tough to play.  I am impressed a high school band handled them.