" Time’s Arrow " Parts 1 & 2 [126th and 127th episodes] show how Guinan met Picard.
Star Trek:
The Next Generation - " Time’s Arrow " Parts 2
[Season 6
Episode 1] 1893
- Data followed by Guinan and Samuel Clemens, is able to follow the alien shapeshifters to the same cavern near San Francisco, where they discover that the aliens traveled to the 19th century to take advantage of a cholera outbreak, draining the life force from humans in infected areas to give the impression that their deaths were the result of an epidemic.
In an ensuing struggle over a cane-like device used to open the portal, Data's head is severed from his body and Guinan is injured .
As Picard tends to Guinan , the rest of the away team, carrying Data's body which continues to grasp the cane device, follow one of the aliens to the future, with Clemens also following them.
The events described above come from Wikipedia and were alluded to by Guinan sometime before in " Booby Trap "
[Season 3
Episode 6]
when Guinan says, "A bald man was kind to me once, when I was hurting."
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According to the episode "best of both worlds" they are beyond friends, beyond family.
That would suggest a deep personal involvement, possibly romantic.
Or at the very least an extremely close trusted friendship.
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TNG Season 2
Episode 1, Wesley Crusher asks Guinan about Picard, and she said that she never met him until she came aboard.
This oversight may have been intentional to help develop Guinan's character later in the series.
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I suggest that anyone wanting an answer to this question reads the recently published "The Autobiography of Jean-Luc Picard", edited by David Goodman.
In this book, although it may not be canonical Star Trek, their friendship begins when, as a member of the crew of USS Stargazer, Picard saves Guinan from bounty hunters
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The closest we get to a description of what events actually made them close is in "Engisn Ro", where Guinan tells Ro that when she was in trouble, Picard helped her.
But presumably there was a lot more than that over a long friendship.
There are no other details given.
The events depicted in "Time's Arrow" don't shed much light on their relationship, it's just Picard insisting that yes, they really will be super close in the future.
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Guinan once said that she's attracted to bald men because one helped her when she was hurt
, most likely Picard, and the first incident (probably one among many) was portrayed in Time's Arrow part 2.
Some of their relationship is posted in various novels, but they're not considered canon.
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In the show they often allude to the history between Guinan and Picard but, to my knowledge, there has never been anything more than allusions.  What exactly happened that created this bond between the two?
What is Guinan and Picard’s history?
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<star-trek><star-trek-tng><jean-luc-picard>
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In "Time's Arrow", Picard insists that they really will be super close in the future. In "Best of Both Worlds" they are beyond friends, beyond family.  Picard said that he had helped her when she was in trouble. Guinean and Picard had a relationship that went beyond friends and was either romantic or familial.
Guinean and Picard had a relationship that went beyond friends and was either romantic or familial.