Will,
If you are not soloing, then I believe you can play chords with either hand, as you accompany the choir, or soloist. But you should probably view both hands together as one chord, in terms of the harmony.
I am not an expert, but I believe it's called "comping" when you do this, although that may be a jazz term.
Maybe someone more knowledgeable can expand on what I've said.
HTH,
God bless,
Eggs