need help

I rent my home and have a gas furnace exhaust chimney problem.
Our furnace is in the living room in front of the exhaust chimney.
When the temps get lower than ten degrees outside and then warms up
we have a dark, sticky, liquid tha runs down the walls surrounding the chimney.
When looking at the chimney in the attic it is sweating the ooze that we see on the walls.
Any idea what our problem nay be? or what we can do to fix it? have pics if you need to see.

here are the pics of my setup and the crap thats comming down my walls, it's not flamable but its sticky, and has no real oder, but when it warms up outside it stops running down the walls, and if you leave it alone it will soon dry up and disappear