The place I live doesn't have sliding windows so I thought maybe I could vent the hot air from the portable AC through the chimney? The chimney belongs to the fireplace that I don't use. (I've not bought the AC yet.)
Yes, it works, I've done it.
It's much more efficient and effective to vent the hot air out a chimney - this is what the chimney was designed for - than to open a window for the outlet. Opening a window as per the usual instructions creates an uninsulated opening to the hot outdoors, leading to heat entering your house even as you try to cool it.
So long as the chimney is sound, and penetrates through the roof (some old chimneys may be sealed off if no longer in use), it's a good option. Try to jam the vent pipe up as far as you can to make sure the hot air goes up.
If it is truly a traditional fireplace chimney and your AC unit has a flexible exhaust hose you could use the fireplace. Like mentioned above, make sure you are the only one who uses the fireplace. Sometimes water heaters and furnaces in older homes will be vented through the chimney. I would think using a piece of wire you could secure the flexible vent hose to the flu vent up inside the so the warm air could go right up the chimney.
You can, but ONLY if it's a less efficient single vent exhaust unit. If the unit has two hoses, one is for cool air intake (to cool the coils) and the other is to exhaust the hot waste air. A single hose unit is less efficient because it takes the cooler inside air to cool the coils, meaning you're wasting energy taking the previously cooled air to cool the coils. If you have a dual hose unit, I would suggest installing a vent to the outside to bring in cool air (like dryer rigid tubing). Put a mesh over it to keep bugs and critters out.
The other catch here is if the chimney is dirty. You could knock loose debris off, which could get sucked up in your AC. I would have it cleaned before using it as exhaust.