The First Amendment (1791) of the US Constitution reads, in full:
“Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances.”
The portions of the First Amendment relevant to the debate over the inclusion of the words “under God” are called the “Establishment Clause” and the “Free Exercise Clause.“
The Establishment Clause
“Congress shall make no law respecting an establishment of religion”
Congress is permitted to add the words “under God” to government materials because the phrase does not “establish” any specific religion.
Congress cannot add any reference to “God” or religion to any government materials because this clause explicitly forbids any such inclusion.
The Free Exercise Clause
“or prohibiting the free exercise thereof”
Americans are permitted to pledge allegiance to a nation under any “God” they choose, or to not use any such words at all.
Congress is prohibited from adding the words “under God” because those words may interfere with the free exercise of atheism.