Acu-rite atomic clock squeaks per...

I had the exact same problem, and found the answer on the Chaney Instrument FAQ page. There's no real solution, but here is the explanation:
Q: My wireless weather station periodically beeps, why?
A: Make sure that any alert and/or alarm features are deactivated first. Constant, sporadic beeping is generally due to the unit’s ability to detect a foreign radio frequency of another wireless unit when that unit transmits a signal. Wireless devices that may cause beeping but are not limited to these devices are; scanners; computers w/wireless keyboard/mouse; or other wireless weather instruments. Essentially, any wireless devices transmitting on a radio frequency have the potential to interfere with each other. Limit the amount of wireless devices to lesson the chance of interference. When beeping occurs, one device will need to be deactivated.