It's the weirdest thing. The outlet began chirping/squeaking intermittedly about 2 weeks ago. Both outlets supply electricity i.e. they work. But it's quite annoying. And I don't know if this is dangerous. It sort of sounds like the chirping of my smoke alarm, but not as loud, when it wants a new battery. Any thoughts?

There is probably a loose connection. Have it checked and repaired ASAP. Loose connection creates heat. That is what I think you hear.

Please have it replaced immediately. Have the wiring in that box inspected by a qualified electrican. You may be hearing what is known as an arcing fault.

I had a Customer that had swiches that meowed. I came over, removed the wall plate, she asked what we should do, I said we will have to cut the wall open, and get the Kitten out.
Their Cat had Kittens in their attic, and one wandered and fell through a small space, and landed on a Cat(Fire block).
If not a smoke detector, turn off your breakers and see if the noise stops.

Stacy, I wonder if you found the above answers correct or something else? I recently began having the same issue in a home I just moved into.