Yes, the right is not 'given' to us by the Constitution, or anyone other than God (the Creator) himself. It is understood to be a natural right that is part and parcel of each individual as a human being. Each person owns his or her right. The Founding Fathers 'discovered' or 'recognized' this fact and wrote it into the Constitution but, more importantly, into the Declaration of Independence. They understood rights so well that they stated clearly that the only purpose of government is to secure those rights.
"… they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. — That to secure these rights, Governments are instituted among Men…"