I'm in the process of researching this problem myself. I have a newer falcon chip 360 with a BenQ drive. at seemingly random times the 360 will make a beep noise, seemingly internal. now I know everyone says there's no internal speakers, and I certainly didn't see one when I opened it up myself but the sound really sounds like it's coming from the 360 itself and not from my surround sound system. I'm using an optical cable for digital audio... however I've also gotten the beep noise when it was connected to an old tube tv at my brother's house using the standard RCA cables so I'm POSITIVE the 360 is making the noise and not another electronic device.
Ever since I've been paying attention to the beeping, it always seems to happen during Divx playback, either via disc or streaming. This sound never happens when I use my elite model for Divx playing.
Any googling research I do on this subject seems to result with people going 'you're crazy' or 'it must be something else' but I know there's definately a small minority of people who's 360s are making beeps!!!
oh and also when the beep happens, there's no otherwise type of distortion in the video nor does it reproduce the sound if I rewind the video to when the beep happened. My 360 has never freezed or 3RODed.