[Sophia the Thunder Mistress]

Actually, a careful reading of the passage will show you that the Elessar did come (indirectly) from Arwen. Here's the passage:

Then she (Galadriel) lifted from her lap a great stone of a clear green, set in a silver brooch that was wrought in the likeness of an eagle with outspread wings; and as she held it up the gem flashed like the sun shining through the leaves of spring. 'This stone I gave to Celebrian my daughter, and she to hers; and now it comes to you as a token of hope. In this hour take the name that was foretold for you, Elessar, the Elfstone of the house of Elendil!'

Then Aragorn took the stone and pinned the brooch upon his breast, and those who saw him wondered; for they had not marked before how tall and kingly he stood, and it seemed to them that many years of toil had fallen from his shoulders. 'For the gifts that you have given me I thank you,' he said, 'O Lady of Lorien of whom were sprung Celebrian and Arwen Evenstar. What praise could I say more?'

So, the stone was originally Galadriel's but passed down to Celebrian, and then to Arwen. Galadriel is simply the deliverer of this gift, not it's giver.

So yes, Arwen did give Aragorn a jewel (though not a necklace, a brooch). But I believe the pendant we were discussing was the white jewel she gave to Frodo.

Sophia