Which amendment to the Constitution protects a citizen's right to speak out against the government?

The first amendment protects the citizens right to petition.

The First Amendment to the United States Constitution prohibits the making of any law respecting an establishment of religion, ensuring that there is no prohibition on the free exercise of religion, abridging the freedom of speech, infringing on the freedom of the press, interfering with the right to peaceably assemble, or prohibiting the petitioning for a governmental redress of grievances. It was adopted on December 15, 1791, as one of the ten amendments that constitute the Bill of Rights.