Other players can click on the NPC or your character to "listen in" on the conversation, but can't take part in it unless it's prompted. (They can also scroll up to read what they missed).
I believe there's also a tab where you can read ALL the previous conversations that took place since the start of the game.
What makes a great Chimichanga?
Hot, thick, 9-inches-long, firm, moist on the inside, easy to grip and less than 8 dollars.
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