My Thanksgiving company left and I unscrewed the vacuum vent cap (or whatever you call it). I ran the water and there was no gurgling sound when I turned the water off like there was before, so off to the hardware store I went to get a replacement.
I got one for $2.99, screwed it in and now there is no gurgling sound. Everything is quite as a mouse.
Thanks everyone for the help. I don't think I would have figured this one out for myself.
I got this one at a hardware store in a little town of less than 8,000 people. Since the device was that easy to find, I decided not to bother with keeping a spare. I probably wouldn't be able to find it when I needed it anyway.
