Can you vent a portable AC's exhaust through the chimney?
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.