This just in, from their FAQ page (emphasis mine):
Who is Hildebrand?
Hildebrand is a celibate, male, baptized Roman Catholic, member of the Church at Rome, of adult age and free from all ecclesiastical censure. He is not a Bishop, so must be consecrated before he begins his papal ministry. His identity will be made known at the time of his consecration, so that until that time he can freely speak with Bishops and they with him, without threats of persecution or harassment. While this might not please his enemies or those who are addicted to curiosity, the pope elect has the right to conduct his own affairs and make his own personal decisions regarding his personal security. Anyone who is sane and rational can see that; and, thus, the Faithful are asked to be patient regarding the divulging of this information.
It is ambigious as to whether he is a priest or a layman, though if he is the latter, obviously he would have to be ordained first (note that they say "consecration", only bishops are consecrated).