High Frequency Noise from Headphones Out Jack

I have isolated the following issue to audio that is monitored via the headphones output on the back of my iMac:

I've been encountering a very high-pitched (and at times a cycling through high frequencies) noise when working with headphones to monitor audio. It's not the headphones and the problem is not limited to any single application. The noise is sometimes barely audible, and it comes and goes - but repeatedly and often. Sometimes the frequency of the noise is so high that I can imagine that those with poor or compromised hearing wouldn't even notice it. But the highest frequencies are still detectable - kind of like a faint ringing in the ears or a ringing television set that has its volume turned all the way down.

I've done everything I can imagine to troubleshoot the problem including asking a Mac genius, but nobody seems to have encountered this before. The noise can be triggered off (not masked) by any other incoming audio, but eventually it reappears. I will be editing a file, the noise will appear, and I can literally silence it for the moment by pressing a volume key or playing back a portion of audio.

Anyone else experiencing this issue? Is there a fix? I do a lot of audio engineering and this problem is very distracting. I haven't purchased any outboard gear to monitor with yet, so I don't know if I will hear this noise through an external audio interface or not. Thankfully, this noise isn't being recorded to disk. It appears to be a little monster that is haunting only the playback.