A Theological, Moral and Political Question about Chimeras

I was listening to one of my favorite radio shows, Radio Lab on WNYC, on my IPod shuffle and heard a story about Chimeras. Chimeras are humans (or other animals) with two separate and distinct DNA strands. Apparently, very early in a pregnancy with fraternal twins, the two embryos can meld into a single entity. That entity has two DNA codes which each take over different parts of the person (e.g. blood, kidney, liver, etc.). This has led to a question in my mind? If life begins at conception, then prior to the melding, there are two humans at the very early moments of pregnancy. But then, very soon thereafter, there is only one individual person who is carried to term and grows up. My question is this - what happened to the other person? Or are there, theologically, two "persons?" If human life begins sometime after the melding, there is no such issue. I don't mean this as a criticism of the "life begins at conception" idea. This is a question about which I am really curious.