Oops, duh, looking at this a little closer (I must be a bit stupid, lately I have a bad habit of misreading things):
I see you have been messing with AO already.  Is Visible in Raytracing checked in the necklace prop's properties?  I believe that's required for AO to work with that object.
Is there any Translucency on the material?  This will allow light though, even if the object appears to be opaque.  Same for transparancy obviously, but the necklace has no appearance of transparency to it.
AO needs to be on for both the light and the material.
Is Casts Shadows checked for the necklace prop's properties?  This may not be required for AO to work, but it shouldn't hurt either, in my opinion, you'll just get a bit more intense shadow if anything.

I'd expect it's one of these things, I can't think of anything else that would make something fail to cast any kind of shadow at all.  Attached link was done with Casts Shadows on for the ring, and AO on the skin and in the main light:
http://www.renderosity.com/mod/gallery/index.php?image_id=1404479&member

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