Some modern electronic equipment can make those 'chirping' kind of noises. Especially the kind that have batteries in them.
Look into computers with backup power supplies, fancy stereo systems, digital TV's, VCR's, DVD players, wireless phones, thermostats with timed settings, etc.
Generally, any electronic device where you enter something (set channels on the TV, set time in the VCR, choose a frequency for the wireless phone) and it is remembered when you turn the appliance off has a battery in it somewhere. Many are the rechargeable type, that will work for months or years before wearing out. But eventually they wear out, and will no longer hold a charge. Often, the device detects this, and makes a warning sound to indicate the battery failure. And often it only sounds off periodically, so it may be hard to find. Sometimes you only hear it at night, when the house is quiet. And it's quiet again by the time you get out of bed and search around for the sound. This can be very frustrating!