Final answer:
Jefferson's claim in the preamble is that people have unalienable rights such as Life, Liberty, and the pursuit of Happiness, and they can establish a new government if the current one fails to protect these rights.
Step-by-step explanation:
Thomas Jefferson's claim in the preamble is that people are endowed with certain inalienable rights, and if a government does not protect these rights, the people have the authority to overthrow it and institute a new one. The preamble of the Declaration of Independence, a document significant to the history of the United States, outlines Enlightenment principles about universal human rights. It states that "all men are created equal," emphasizing the unalienable rights to Life, Liberty, and the pursuit of Happiness.
Moreover, it stipulates that governments exist to secure these rights and should operate with the consent of the governed. Jefferson, despite being a slaveholder, included these radical ideals in the document, which were based on John Locke's theories of natural rights and the social contract.