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"The One with the Jellyfish" (Season 4, Episode 1)
Chandler and Monica hang out on a beach and he asks her if she'd go out with him in the event of a nuclear Holocaust and he is the last man on Earth. She replies, "Eh." Joey is there too and he and Chandler then witness Monica getting stung by a jellyfish. Joey suggests an effective but unsavory solution, and Chandler ends up implementing it. This episode was brought to you by the letter P.
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"The One With Ross' Wedding" (Season 4, Episode 24)
The two hook up at Ross and Emily's wedding, but want to keep it a secret from their friends. "We're gonna see each other naked!" Monica says. "Wanna do it at the same time?" Joey then almost walks in on them.
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"The One Where Phoebe Hates PBS" (Season 5, Episode 4)
The two keep their relationship on the down-low, while Chandler gloats after Rachel says that Monica told her her secret boyfriend is the best sex she ever had
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"The One Where Everybody Finds Out" (Season 5, Episode 14)
The title is self-explanatory.
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"The One In Vegas" (Season 5, Episode 24)
In this two-part episode, the two split temporarily on their one-year anniversary of dating, but later reconcile and almost get married.
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"The One With The Proposal" (Season 6, Episode 24)
The two propose to each other!
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"The One With Monica And Chandler's Wedding" (Season 7, Episode 23)
Mazel tov!
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"The Last One" (Season 10, Episode 17)
In the two-part series finale, which aired in May 2004, Monica and Chandler adopt a twin boy and girl, Jack and Erica, named after Monica's father and the children's birth mother.