Yes. That is the alternating diamond and pearl necklace that Queen Mary wore often, bequeathing it to Princess Margaret in 1953, who added a detachable pendant, it is now worn by Lady Sarah Chatto.
The origins of how Queen Mary acquired it are unknown, however due to the abundance of diamonds and pearls in her collection, if it was not a gift, it is likely that it was a commission using her own stones.
--Previous Message-- : : Thank you all. : Now would the second necklace here be the : one now worn by Lady Sarah Chatto? : : : :