I've performed "Jenny" with friends a couple of times, and I think I have a viable chord reading, at least for what Bret plays on the HBO special (I have no idea what Jemaine does).
Note that the tab chart below is my adaptation of slightly incorrect chords I found at
http://www.azchords.com/f/flightoftheco ... 18069.html, in which the fourth chord is incorrect. The rest of the chords I just figured out from watching the FOTC clip. Also note that I'm not sure how to use a monotype font, so spacing is probably off.
At the start of the song, these four chords repeat (you can see Brett's hands if you watch closely):
e|--------10-----------x----------9------------10-------------|
B|--------10-----------x----------10-----------12-------------|
G|--------11-----------11---------11-----------12-------------|
D|--------12-----------11---------11-----------12-------------|
A|--------12-----------12---------9------------10-------------|
E|--------10-----------9----------9-------------10-------------|
The first is an E barred at the 10th fret, followed by the same chord with the bass note raised a half step (and the G&E muted), then an Am barred at the 9th fret, and then an A barred at the 10th fret.
At a few key points in the song, you play what nearly amounts to the same four chords, only up higher on the guitar neck (lower pitch): a normal D, followed by a normal A, then an F#, then a G (but instead of a normal G, you slide up a half step from the F# so that it's an E barred at the third fret).
Those two 4-chord progressions are interchangeable, so I think Brett just switches back and forth at key points in the song to add some variety.
There are two points in the song where the chords are different. I'm pretty sure I don't have them exactly, but here's what I play:
---------Bm---------------A
You said, "Meet me here in one year"
------G-----------------------A
You just needed some time to clear your head
(Then you return to the 4-chord progression on "head").
And later:
----------D---------Bm
We just looked -- oooouuuut
----A----------------------------G--------------------------A
Across the city from our little spot up there on the hilltop.
------------Bm---------------------------A
Oh, it's so pretty from way up there.
-----------------------------Bm------------------------------A
We talked about how the lights from the buildings and cars
------------------G----------------F#
seemed like reflections of the stars
------Bm------------------[no guitar]
that shined out so pretty and bright, that night.Â
I'd love to hear corrections if anyone has some, but hopefully these will do as a start for anyone who want to learn the song.