I've been noticing what sounds like a short, high-pitched electronic chirp coming from the passenger side dash of my 2002 Intrigue; the only thing I can compare it to is the chirp from a cheap digital watch marking the hour.

There doesn't seem to be a particular pattern or certain time when the chirping occurs, just happens randomly, but it does seem to happen more frequently when it's cold outside.

Any idea what I might be hearing? Possibly two pieces of plastic rubbing together?

It's probably your blower motor. What speed setting is it on when it chirps? Usually a sign of a going blower motor is when it squeeks or chirps at the lowest settings.

But just because it squeeks doesn't mean it's going to crap out right away...mine has been squeeking since November.

Probably the blower motor. Turn the vent settings to OFF and see if you still hear the noise.