|: C# minor | F# majorE major | G# major :| C# minor
(This is basically what The Beatles Complete Chord Songbook lists, too.)
The F# major and G# major are a bit out of place, since both contain accidentals (the A# in F# major and the B# in G# major). Normally in E major, the chords built on F# and G# are minors, but I think it's significant that these two chords are major.
The lyrics for this section are:
In my mind, there's no sorrowDon't you know that it's soThere'll be no sad tomorrowDon't you know that it's so
Minor chords are often perceived as sad, but since "there's no sorrow" and "there'll be no sad tomorrow," these normally minor chords are transformed here into major chords.