If you hear a chirping or sharp screeching noise emanating from the unit, the condenser fan component might be striking the fan housing. A condenser fan obstruction not only creates noise, but it also strains the blowing potential of the entire unit. After the electricity is shut off at the breaker, you can remove the fan housing panel on the outside of the unit to examine the condenser fan area. Spin the fan blades around manually to see if they make contact with the side of the fan housing. If they do, the fan is improperly mounted. The fan can be reinstalled correctly to eliminate the noise.
Oddly slanted or split ductwork can cause a whistling noise during air conditioner operation. Holes in the ductwork can create the whistle as air blows through it, just like a mouth creates a whistle. With the unit turned on, you can look for these holes along the ductwork in the attic or crawlspaces of the home. The holes can be patched up with duct tape or the ducts fully replaced to correct the noise.
Grimy or dry ball bearings can cause an occasional shriek or chirping noise as the fan component revolves. The situation not only causes a racket, but it also builds up resistance in the fan, causing it to under-perform or possibly stop altogether, which strains the fan motor and might lead to a burn-up. After the fan-housing panel on the unit is removed, you can twist the fan manually to check for resistance in the ball bearings. Under proper conditions, the fan should spin freely. Electric motor oil can be poured into the ball bearing chamber through the lubrication ports along the axle. A few turns of the fan will work the oil into the bearings, which should eliminate the noise.
Not uncommonly, a small bird or other animal will find its way into the ductwork or even the air conditioner unit and get trapped. For this reason alone, electricity to the unit should be shut off immediately upon hearing an unknown noise. You can remove the fan housing panel to search the unit for creatures or foreign objects. Debris, such as plastic bags and sticks, can get stuck in the gears of the unit in such a way as to make all kinds of noises and should be removed.