Typically that is caused by a warped brake rotor and the caliper is sliding back and forth on its mount. That is not serious and will be addressed the next time the brake pads need to be replaced. Your mechanic will machine the rotors to make them true, or if they will end up thinner than the published legal limit, he will replace them. The clue is the chirping will only occur when going forward.
The rear drum brakes can cause a chirp too but it's not as common. The chirping will occur going forward or in reverse.
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Sunday, April 21st, 2013 AT 4:26 PM