Faint chirping at startup = A/C compressor?

Everytime I start my 2001 XJ sport, 4x4 auto, I hear a faint, rythmic chirping (~twice per second) coming from, I think, the passenger firewall area under the hood. The Cherokee is stock condition, has 88k miles and everything works/runs fine. The chirping isn't affected by vehicle speed or engine RPM's. It goes for about 30 seconds then tapers off. Anyone have any idea what this might be, and how to make the chirping noise stop?

Thanks in advance for your replies.

loose belt or rusty bearing

ehall said:

loose belt or rusty bearing

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I would normally agree, but the rythm of the chirping does not get faster if I rev the engine, or increase my speed. That's why Im confused what it might be.

Get a length of heater hose and use it to probe for the sound if you can. I had my distributer(brass bushing) cause an odd chirp that surprisingly didn't change with RPM that I remember. With the heater hose you should really be able to narrow down the sound though.