Corrected entry: When Elizabeth is talking with Norrington before she falls to the sea, she is wearing two necklaces - a short gold necklace with white pearls, and a long chain with the Aztec medallion. Later, we see only the chain with the Aztec medallion and there is no trace of the other necklace. (00:10:55 - 00:15:40)
Correction: The other necklace was a much more delicate piece than the sturdy chain for the medallion. Considering the height from which Elizabeth fell, chances are it broke when she hit the water.
Sereenie