1 Peter 2:7-9
7 Unto you therefore which believe he is precious: but unto them which be disobedient, the stone which the builders disallowed, the same is made the head of the corner,
8 And a stone of stumbling, and a rock of offence, even to them which stumble at the word, being disobedient: whereunto also they were appointed.
9 But ye are a chosen generation, a royal priesthood, an holy nation, a peculiar people; that ye should shew forth the praises of him who hath called you out of darkness into his marvellous light:
5 Now therefore, if ye will obey my voice indeed, and keep my covenant, then ye shall be a peculiar treasure unto me above all people: for all the earth is mine;
6 And ye shall be unto me a kingdom of priests, and an holy nation. These are the words which thou shalt speak unto the children of Israel.
The obvious point is that although God referred to the believers in Israel as a “Kingdom of Priests”, only the Levites would actually become priests. Likewise, if Peter is correctly quoting God (and we must believe that he is) then the ancient Christian Church could be a “royal priesthood” without requiring that every Christian be a priest. Instead, like ancient Israel, certain worthy individuals held the priesthood and the entire Church was blessed by them.
John Tvedtnes writes more about this issue here, which I highly recommend: http://www.fairlds.org/Bible/Is_There_a_Priesthood_of_All_Believers.html