It's most likely a slightly defective fill valve that may have a bad seal or a piece of grit stuck in it. You can probably confirm this by taking the tank lid off when it does this and pull up on the floating ball in the tank a little. If your toilet has a fill valve that doesn't require a float, pull directly up on the flush valve at the left. The sound should stop.

The simplest solution is to start getting handy. A new valve costs about $7 and takes maybe 15 minutes to install. It comes with step-by-step instructions that any adult should be able to follow. Or you could pay a plumber $100 for the same job.

I would change the flapper too.

Thanks for your advice and suggestions. The plumber replaced the fill valve, flapper, and broken supply line (stop valve) 6 months ago.

I was positive the flapper was not leaking so I began tinkering with the fill valve. I found out how to take the top off and let the water run to clean it out any debris. Then put back together and it still hisses.

I already replaced the fill valve, flapper and stop valve in another toilet (after watching the plumber - I know enough to be DANGEROUS!), but I really didn't want to have to do it again on a toilet that just got new parts 6 months ago.

I got so frustrated yesterday that I thought, what the heck, just buy a new $4 flapper and see if that's it. I was sure that it wasn't, but alas, it has ceased sizzling, hissing, and flushing itself.

Again, thanks for your help. I was so sure it could not be these new parts, but didn't want to miss anything. Perhaps my water is so awful that I'll need to replace the flapper every 6-9 months.

cstleddy-
It's easy for a flapper to seal (almost) perfectly, but still let a tiny bit of water continuously ooze through, and then the hissing starts when the water level gets a little low hours later. If you have this problem again, check the rim of the flapper and the rim of the outlet for any grit before bothering to replace the flapper. I once had this problem, and realized there was a tiny porcelain "pimple" about the size of a grain of sand on the top side of the outlet. I used a piece of sandpaper to remove the defect and solved the problem.

Thank you for telling us your fix. If it happens again, reread the previous post. You may have to change that entire seat, which entails removing the tank.

There's an alternative to removing the tank to replace a flush valve and seat if it keeps leaking. The Fluidmaster 555C "flush valve repair kit" (which is a flapper with it's own seat) installs directly onto the old one.