Have you tried to bang around with a rubber mallet yet? Your noise cannot be caused by any revolving mechanical part since the cadence does not change with change of speed or engine RPM. Are you positive the cadence of the chirp does not vary? You either have a metal to metal squeak brought on by a specific vibration caused by the running engine, or someone with a high degree of ingenuity and access to your vehicle has installed an elaborate electronic squeaking device which only comes on when the engine is running. I do not know you, nor live anywhere near you, so it wasn't me. Besides, it is much easier to drive someone batty by putting a zip tie on the drive shaft with the long tag end left on to smack the floor board.
Carl
