In episode 21 of THE iDOLM@STER, Chihaya sings Nemurihime solo at a concert. Thanks to President Kuroi's interference, the technicians won't start the music, so Chihaya decides to sing a cappella (i.e. with no accompaniment). They do start the accompaniment at the first chorus, so it doesn't stay a capella the whole way through, and furthermore the song is cut (the full duration is 5).
The video from the anime is here. Note that this video contains major spoilers; in fact, this scene is basically the climax of the anime. In case you want to avoid any spoilers, the full version of the song from one of the CDs (with accompaniment throughout) is here.
Was a full a cappella version ever released on any of the CDs, or in any other form?