According to the change log for Terraria 1.3.2 (emphasis is mine):

Parties have now been added! You can start your own via the Party Girl's Party Center or the Town NPCs may start one, if certain conditions are met

What conditions must be met for a party to naturally occur? The wiki entry on the Party event doesn't list anything specific.

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1 Answer

According to this link, a party has a random chance of naturally occurring at dawn, and no conditions need to be met for a party to be naturally hosted- but I'd guess you'd need at least one NPC in your world to act as the host for a party.

Edit: I've tested the theory and have conformed that a party can naturally occur in a world without the need for a party machine. The world I used was a small, non-Expert mode pre-hardmode world. The only NCPs that had moved in were the guide, merchant, dye trader, arms dealer, demolitionist, nurse, painter, clothier, mechanic and dryad.

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