My money is on fan belt. Check your pulleys are aligned correctly and belts are tight.
If a belt is loose and for example, your battery is a bit low, when your engine starts it will draw a lot of current to charge it and this loads the pulley a LOT and the chirrup you hear is the belt slipping on the pulley. Same goes for power steering at full lock with a loose belt.
If your fan belt is really loose, the cooling fan will cause it to squeal.