Repeated noise coming from a GFCI outlet

I have a GFCI in my kitchen that seems to keep making a clicking noise. The GFCI is connected to one other outlet along the countertop. The funny thing is that it keeps doing this every 15 minutes or so even after it has tripped off (without me reseting it). This is the same noise as if it is tripping from the on to the off state. This is all happening while nothing is plugged into the outlets.
I have tested that the GFCI is working by plugging a light in and the light works when the GFCI is set, but turns off when I press the test button.
Is it a bad GFCI outlet?
Is this some way of indicating to a person that it has tripped by making the noise?
Is there something wrong with the wiring that I need to take a look at?
Any advice or other thoughts are appreciated.
-DK
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Dan Koellhofer wrote:

Almost certainly. If it is really still trying to trip after it has already tripped and hasn't been reset, it is sensing a ground fault where it should be impossible for one to exist.

No. New GFI outlets now come equipped with a LED for that purpose.

Possibly. However, it sounds more like a defective GFI. Spend $12 on a new GFI first.
See also: http://dotznize.com/electric/?a=gf
--
Best Regards
Anthony Straight
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