It's not a fake - it is indeed a very old chalice, but probably not the original one used at the Last Supper. However, there is some suggestion that it was used in Rome for the celebration of the Eucharist very early in the history of the Church, and then eventually ended up in Spain (which was a Roman territory) during a 3rd century persecution.
There is another chalice in Spain, known as the Holy Grail of Galicia, in the 9th century church at O Cebreiro, a steep and foggy mountain known for the bad weather at its summit. This chalice is famous for a miracle: during a storm, a devout peasant came, as usual, to attend mass. The lazy and faithless monk didn't want to be bothered and said to himself the equivalent of, "oh, here comes that stupid peasant again, out in the storm, just to see a piece of bread and some drops of wine." And then the bread and wine turned into the flesh and blood of Christ before the monk's very eyes. The chalice and paten (which are 12th century) are preserved and visible in a glass case in the church.
So in other words, there are various ways in which something can be a sacred chalice or Holy Grail, if not "the" Holy Grail.
I was just given a nice explanation that the top part was the original part (made out of stone).
The rest was added and that makes sense to me.