No, there is no "wall of separation" clause, but there is an "establishment clause" in the First Amendment that has been interpreted by the Supreme Court since the late 1940s as meaning there is be a separation of church and state.Actually the interpretation dates back to 1878, and Reynolds v. US:
At the first session of the first Congress the amendment now under consideration was proposed with others by Mr. Madison. It met the views of the advocates of religious freedom, and was adopted. Mr. Jefferson afterwards, in reply to an address to him by a committee of the Danbury Baptist Association, took occasion to say: "Believing with you that religion is a matter which lies solely between man and his god; that he owes account to noneother for his faith or his worship; that the legislative powers of the government reach actions only, and not opinions, -- I contemplate with sovereign reverence that act of the whole American people which declared that their legislature should 'make no law respecting an establishment of religion or prohibiting the free exercise thereof,' thus building a wall of separation between church and State." Coming as this does from an acknowledged leader of the advocates of the measure, it may be accepted almost as an authoritative declaration of the scope and effect of the amendment thus secured. Congress was deprived of all legislative power over mere opinion, but was left free to reach actions which were in violation of social duties or subversive of good order.
-Eric