"The Omega Glory". The conceit of the episode is that the Enterprise arrives at a planet where the blond-haired, light-skinned "Yangs" are brutally oppressed by the vaguely-Asiatic "Kohms." As always happens in these sorts of situations on Star Trek, the oppressed eventually rise up and overthrow their oppressors.
At first it looks as though the Yangs aren't going to be any better to the Kohms than the Kohms were to them. However, it transpires that the Yangs' holy document is the American Constitution1, garbled through centuries of oral tradition; Kirk recognizes the words, and ends the conflict by giving a stirring speech about equality, quoting the correct words:
Cloud: Greatest of holies. Chiefs and sons of chiefs may speak the words, but the Evil One's tongue would surely turn to fire. I will begin. You shall finish. Ee'dplebnista norkohn forkohn perfectunun.
Kirk: Those words are familiar. Wait a moment.
Cloud: When you would not say the holy words, of the Ee'd Plebnista, I doubted you.
Kirk: I did not recognise those words, you said them so badly, Without meaning.
Elder: No! No! Only the eyes of a chief may see the Ee'd Plebnista.
Kirk: This was not written for chiefs. (general consternation) Hear me! Hear this! Among my people, we carry many such words as this from many lands, many worlds. Many are equally good and are as well respected, but wherever we have gone, no words have said this thing of importance in quite this way. Look at these three words written larger than the rest, with a special pride never written before or since. Tall words proudly saying We the People. That which you call Ee'd Plebnista was not written for the chiefs or the kings or the warriors or the rich and powerful, but for all the people! Down the centuries, you have slurred the meaning of the words, 'We, the people of the United States, in order to form a more perfect union, establish justice, ensure domestic tranquillity, provide for the common defence, promote the general welfare, and secure the blessings of liberty to ourselves and our posterity, do ordain and establish this constitution.' These words and the words that follow were not written only for the Yangs, but for the Kohms as well!
Cloud: The Kohms?
Kirk: They must apply to everyone or they mean nothing! Do you understand?
Cloud: I do not fully understand, one named Kirk. But the holy words will be obeyed. I swear it.
Star Trek Season 2 Episode 23: "The Omega Glory"
The fact that this episode ends with a Canadian waxing poetical about the cornerstone of the American political system2 is something I shall mark politely, and leave for your consideration.
1 In fact, it turns out that the whole planet is an alt-version of Earth, where the space-Russians won the space-Cold War; "Yang" is speculated in the episode to be a corruption of "Yankee" and "Kohm" a corruption of "Communist".
2 To another Canadian, as it happens.