The Cohen, you will recollect, were the priest caste of the Hebrews. They were the ones charged with the care of the Ark of the Covenant. Only Cohenim were permitted by Yahweh to enter the sacred presence of the Holy of Holies without being immediately stricken dead.

Membership among the Cohen was hereditary, and passed from father to son. Geneticists have identified the gene associated with the Cohen tradition, and can test for this in the population at large. The presence of this gene is passed down from male to male, and denotes a common ancestry -- Aaron, if the stories are to be believed. In fact, this knowledge has been used to clarify certain bizarre historical oddities, such as that sub-Saharan African tribe who all claimed to be of ancient Jewish descent, despite the fact they were quite black. (The test actually confirmed the presence of the "Cohen gene" in a significantly high portion of the male population of that tribe. I believe they are called "Beta Israel.")

Now, as I was saying, the "Cohen" gene — and therefore, membership in the Cohen caste — is transmitted from father to son. However, traditionally, membership in the community of Judaism is transmitted matrilinearly, from mother to son or daughter. In other words, if your mother was Jewish, you're Jewish, end of story; if your mother was shiksa, it really doesn't matter what your father is, because you just ain't Jewish — end of story.

So it's theoretically possible for a man of the Cohen caste to marry a shiksa. This union could produce a son. This son, being born of a shiksa, would not be Jewish — he'd be Goy as Caesar. But he would still be Cohen, because he'd be the son of a Cohen.

Weird, eh?

Wrong. Every mother going back to Aaron must be Jewish or the son does not have Cohen status in the Jewish community, regardless of whether or not he is a descendant of Aaron.