How do I stop Robertshaw thermostat from making load chiping noise?

Hi! beastonator, and welcome to AMHD :)

There's nothing in them that chirps, unless it's my second suggestion.

Two things to check:

Do you have a smoke detector overhead in the immediate vicinity of the thermostat?
Battery powered smoke detectors or hard wired smoke detectors with battery backup
Have a low battery indicator that chirps.

Do you have a digital programmable thermostat with a battery backup?
It may also have a chirping signal to indicate a low battery condition.

K