What would DA do?  

Keeping the full length, I'd opt for a sofa table or console upon which you might place lamps and things.
or chop it up for step-stools

Live edge longboard skateboard!

Cut slab table at just outside large dark ring to make a three legged console place fourth leg Under remaining piece and create an extension for the console table
Like this table at Andrew Spindler antiques

Two shelves... or one really long one.

Lovely hunk of wood.
I'd hang it on the wall vertically. Yup.
Best,
Aunt Art.

Not flat ? How ? Cupped -- or crowned ? Flat enough for an occasional or display table ?
Good ideas above. Longboard, indeed -- with monster wheels, maybe . . .
Here's what I'd think you want:

Nice response, SDR.
Keeping the live edge is, I think, exactly what the plank (and Tex) wants and splayed tripod legs are really the only way to go here. Wedged through-tenons are a nice traditional and Nakashima-esque touch, too. AND every operation is easily, perhaps best, accomplished over a weekend's time with hand tools. No electricity, flying dust, or loud noises required.
Maybe it's just the hand-drawn sketch or the obvious thought you've put in, but, either way, I love it!

Well -- a drill press is a quiet tool, I guess ! What's the Cadillac way to go, with those bores -- should they be tapered holes, to accept the wedged tenon and lock the head of the leg in place -- or is that overkill ? Does anybody make tapered drills ?

Sure, Lee Valley Tools offers spoon bits for use in a bit brace made for this exact application. There are tapered reamers available, too. Traditional Windsor chair construction almost requires them.
http://www.leevalley.com/us/wood/page.aspx?p=57713&cat=1,180,42337

I like that... WWDAD (What Would Design Addict Do)
The slender width would suggest to me a console table, or as SDR said, "display" table. We have a client who bought a Nakashima dining table which was quite narrow, more narrow than they wanted for their dining room, but not as narrow as what you typically think of for a console table. They put it in the middle of a room by their entry and used it to display small sculptures, other artworks and art books. Looked great.
I would totally use wood legs rather than introducing another material like metal, and would think about making it a height you could use along a wall as a console, behind a sofa in an open floor plan, or as a long, low bench/ table. It's certainly a pretty piece of wood.

Oh -- the name of your display/sofa table: "Three-legged Walnutfish 1.0"
If it were mine, I'd ponder leaving the board as found, with perhaps a bit of fine sanding and some oil -- or sanding the underside more vigorously, with die grinders and belt sanders, shaping it into a smooth underbelly.
(The great advantage of three legs: the piece will never "rock.")
Whatever you do, enjoy it to the fullest. There's no pleasure like standing back and looking at what you did . . .

You could make something similar to this:
http://www.designaddict.com/forum/General-discussion/Aasbjerg-walking-table
Although I have to admit that with an unstable large slab like that the three legs will never wobble argument is good.

Oh, yes, I liked that table/object. Did you ever try it with the legs repositioned ? Many a designer has probably wished he could present a design in more than one variation . . . !
I never got an answer to the question of the surface of the walnut piece: is it not flat ? What is the texture ?

I wish I owned that table. It sold in New York a while back.