Simplest stuff first. Put the bike on a work stand, grab the right pedal, and pedal backward slowly while listening to the chain as it runs through the rear derailleur. If the chirp happens once every rotation of the pulleys, the chirp is originating there.

If the chirp happens about once every three or so revolutions of the cranks, it's the chain that's chirping.

Lubrication is needed in either case.