Kate wore this necklace out to a club during her early 20s.
The closeup is from My Small Obsessions:
It’s a double strand necklace consisting of small black beads and black/gold beads of various sizes strung in an irregular pattern. It is difficult to see the full necklace because her hair is obscuring it, but I will venture a guess and say the pattern repeats itself throughout the length of the necklace.
It appears that the black beads are faceted, possibly black onyx. This is on a silver chain. I think this is costume jewelry. It could be an Acessorize find, but I’m not sure.