So I just built my new system a few weeks ago, and now while running at idle I will get random beeps.
Short beeps, long drawn out beeps, and chirps. Always loud enough to hear across the room.
 
I didn't see any mention of it in the DG case documentation, but the only thing I can think of is the fan controller in the DG-87 has a beeper on it?
It's either that or something in my system is failing and beeping its death song.
 
Edit: So I contacted EVGA and there is nothing that makes noise on the DG-87, my motherboard the MSI z270 Gaming M7 doesn't make noise either.
That allowed me to narrow it down to a few remaining things in my system and it turned out my Asus EAH5870v2 had a little beeper/alarm right on the end next to the 6-pin and 8-pin power connectors which was causing all the noise. Odd that it just started, but I guess getting around 8 years out of a graphics card was pretty good.