The ethereal sound was created by laboriously building up multiple overdubs of the voices of Stewart, Graham Gouldman, Godley and Creme singing a single note in unison. This multi-track was then mixed down and dubbed down onto 16-track tape. This process was repeated across all sixteen tracks to create a lush 256-voice "virtual" choir that could "sing" chromatic chords. A number of these prepared multi-tracks were then cut into several endless loops, each of which contained the basic notes of the main chords used in the song. The chorus loops could then be played by using the mixing desk rather like a keyboard -- each chord could be sounded by bringing up the fader for that loop.Here's a brief documentary about the creation of the song:
The instrumental break featured the repeated spoken phrase: "Be quiet, big boys don't cry...", which was spoken by Kathy Warren, the receptionist of the Strawberry Studios where the band recorded the track...
In this pre-sampler period, the group was able to simulate a large polyphonic choir, creating a dramatic tonal effect similar to that produced by the well-known choir setting on the Mellotron, but with a far richer sound, and in full stereo.
Addendum: I originally created the above post about 10cc's "I'm not in love" a bit over a year ago. Today an interesting item at BoingBoing prompted me to revisit my post, and I discovered that the first video I had embedded at the top of the post has subsequently been taken down. So I've substituted the one from the Boing Boing post (where there is also an extended commentary and additional links).